Suppose a player misses more than 1 game year. How do you handle Winter Phase for this player? My interpretation of the rules is that the missing player can do a few solo adventures to catch up, although that still leaves him behind the other players. Do you do the each of the missed Winter Phases for the absent player?

Winter phase must always be done. (extra) Solos are optional.

Does that mean that if a player misses 3 game years, he's allowed to do the 3 missed Winter Phases?

Yes

You kinda have to have the Winter Phase for every character every year, because of aging rolls, stable, child survival/production, let alone having the absent knight have a chance of keeping up in personal development with his peers. Greg even has some ideas for supplementary XP etc for characters who weren't present here (http://www.gspendragon.com/catchup.html).