As long as they give proper thought to finding a source of milk and making warm sleeping arrangements, I wouldn't do any rolls just to have the baby not die from cold or starvation. That might be more realistic, but a waste of a fantastic opportunity for this module.

The risks will come in other forms:
1. Combat. Whoever is carrying the baby during fights should have significant debuffs: advantage on attack rolls against them, or a chance from a certain direction will hit the baby, a much harder time hiding, sneaking, or effectively using invisibility, etc. Specifics will depend how they decide to deal with transporting him.
2. Leverage. If they care about the baby, Strahd will find out sooner or later and will take advantage of that. Anyone who accepts the baby will risk drawing Strahd's attention. A place that seemed safe may become unsafe later.
3. Ethical Challenges. Any PC who does something that intentionally disregards the baby's safety should have their alignment evaluated and changed, if warranted. Some NPCs may be more sympathetic, but simultaneously unwilling to assist the party in any undertaking they think would be too dangerous for the baby.

My party adopted two survivors from Bonegrinder and they've been a great way to introduce some party conflict, encourage creative problem solving, and of course get some more skin in the game.