A lot depends on what crops up in the home inspection as problem areas (e.g. faulty wiring, wet basement), and what's been done recently by the prior owners. Hopefully they'll provide info and the names of their contractors.
DO NOT assume that nothing will go wrong for a while. We have a bunch of new neighbors, and two of them had major plumbing problems (including one where a pipe burst and the ceiling caved in). These were well-maintained homes - but stuff just happens sometimes. Murphy's Law. Plan ahead!
Bleeding radiators? Depends on the type, I guess. I've never done in after decades in this house.
Chimney cleaning - remind your friend that he has more than one flue inside his chimney. One is for fireplace and one is for heat. So even if he never uses the fireplace, he needs to clean the other side due to soot build-up. There are licensed and certified chimney sweep services. Consider a chimney cap to keep squirrels and other rodents out. Nothing worse than a raccoon down the chimney....
Yearly maintenance of oil burner or other furnace. We swear by the annual maintenance contract - they'll clean it once a year, and often service for free with basic parts included. Just one big repair can bust the budget and it's great to have the oil company run out to help for free if you're out of heat. Look into a budget plan with a monthly payment so they don't get hit with a big bill in January and February.
Gutter cleaning - essential after the leaves have fallen so gutters aren't clogged. Water collects, freezes, expands and causes ice dams with cause inside leaks. He might have the gutter person take photos with his phone to show before and after. November is a good time - after leaves are down and before major freezes. For our 8 room house, it's about $85 a year. Well worth it. We sometimes have to do it twice a year because some of our oak trees don't lose leaves until the spring when the new growth pushes the brown leaves down. Watch pine needles too even if there aren't a lot of regular leaves coming down. They are hell! Have the gutter person check for any holes around the eaves - otherwise squirrels happily take up residence in the attic insulation. Do not ask me how I know this! LOL!
Shut off outside water (valves in basement) and open the spigot(s) where you attach garden hoses. Drain and re-close. Take in hoses so they don't freeze. If this has been done already since it's December, have your friend check to be sure the spigots were tightened so he doesn't turn the water on in the spring and have it spurting all over the yard!
Septic tank pumping unless they're on town sewer. How often depends on the number of people in the house and whether or not they use a garbage disposal. Companies will tell you to do it yearly; we've often gone 3 years with just 2 people in the house and composting our vegetable peelings/scraps and not using the disposal. If the tank lid is down deep, the homeowners can save money but digging up the grass/dirt themselves. Just put it on a tarp next to the area and replace it, grass and all, when pumping is done. Do any time of year except when ground is frozen.
Learn about lawn care. Mow it short before winter and get up the leaves; leave it longer in the heat of the summer. Do not water every day, but do water deeply (1 inch down) once a week so roots grow deep rather than spreading out on the surface - the lawn will be more drought resistant and will grow thicker, keeping weeds down. Think hard about fertilizer as it pollutes ground water and local reservoirs; use organic if possible. We have a lot of pines (acidic) so we lime generously (organic limestone) - use pellets, not powder so it doesn't blow all over. Check on local water bans or requirements during a drought.
Understand that you are responsible for shoveling snow from around hydrants on your property (our neighbors all share this job) and from your mailbox if you want mail delivery. Requirements are on Postal Service website. We also have to shovel a path to the oil fill pipe if the snow is deep, including a cut through the "plow pile" at the curb. The delivery guys walk through 4-6 inches but above that, they need our help. Consider a plowing service for driveway and mailbox area, or invest in a snowblower (a good one) if in a northern state. Do not let snow pile up in front of vents. Get carbon monoxide detectors even if they aren't required by law.
Your friend can find tools, yard implements and so on at yard sales. No reason to buy new when someone leaving the area or downsizing is unloading rakes and snow shovels and tarps and so on.
Find out if trash pick-up is provided or if it's private pay. I always assumed it was a taxpayer provided service and was shocked to find out that it wasn't automatic.
Find a good, old-fashioned general appliance repair person who will be the go-to expert for washing machine, dishwasher, everything. Have a good plumber's name in your contacts list because usually when you need one of those professionals, it's usually urgent. Also find a small, old-time hardware store that will sell you a few nails or bolts or washers so you don't need to spring for a pack of 100 at Lowe's every time you need something. They're great at service, in my experience.
If there's an automatic garage door opener, learn what to do in a power failure so you can get in and out.
Consider tipping your letter carrier and garbage pick-up/recycling pick-up person at the end of the year. Small gifts or gift cards under $20 (supermarket, not restaurants) are appropriate - you'll get better service.
Learn about town services and local organizations (Scouts, etc.) that do great things. We have textile recycling (all the clothes and stuffed animals and bedding that are too old/stained to donate, plus broken backpacks/purses), styrofoam recycling, hazardous waste disposal day, prescription and non-prescription drug disposal (please do not ever flush this stuff down the toilet!), Christmas tree pick-up and recycling (chipping into mulch), and a lot more. If the local Garden Club has a plant/shrub sale in the spring, your friend can often get good advice on hardy plants good in his area.
Learn about wildlife. We have raccoons, skunks, wild turkeys (sometimes 20-25 up in the trees at night!), coyotes (so we never, ever leave our small dog outside on a run), deer (choose plantings carefully as they will eat certain shrubs in the winter), and more. Assume that mice will find their way into the house at some point - can't keep them out, just gotta deal with them. The larger animals are around if you have woods, but the mice happen no matter what, and it's not a sign of a dirty house.
Get to know your neighbors! They are your best source of information. Give a key to at least one good neighbor in case you get locked out - there's no superintendent to let you in!
Hope these lists don't scare him off! It's great having your own place - most of the time!