depends on the blanket. My babies always had blankets. But they weren't big thick quilts. They were little plisse (sp?) ones that my mom made. Super lightweight cotton (like a sheet almost) with stitched edges. Then, as the weather got colder, they would have the little baby blankets that were micro fleece. But they were wrapped in them (swaddled).
For enough warmth in winter, they also were in sleepers. They didn't have a pillow until they were in an actual bed, not in a crib. So a minimum of 18 months, but it was probably older. They are 11 & 14 years, now, so I can't remember exactly.
FWIW, in my later years (just in the past year or so), I find that I sleep more comfortably without a pillow at all. I will wake up in the night and feel like my neck is too crooked, and so I just push the pillow up against the headboard and lie on my back without it. And I don't have a big thick pillow---it is down, so it is super soft and squishes down. I just recently noticed that I like it without it sometimes. There really is no rush to provide a pillow to your little one.