Yes. Several listings note attached hoods with faux‑fur trim or faux‑fur lining, and some mention a snug fleece lining around the neck/head for extra warmth.
Most snow bibs include adjustable shoulder straps and back elastic bands so you can tighten or loosen the bib for a better fit as a child grows.
Listings commonly list banded or elastic cuff closures on sleeves and elasticized ankle cuffs or ankle closures on snow bibs to help block drafts and keep snow out.
Snowsuit listings commonly come as two‑piece sets that include a jacket (puffer or coat) plus a matching snow bib.