Motivation: give us access to tree seeds and some nuts and mushrooms in winter and spring. Let the newbies make their cone cows, lizard on scales, mushroom spits, and nutjerky. Let the people doing credo quests deliver or eat some fall items during winter and spring.
You could make it like a bird's nest which has to be rummaged with a countdown timer. Maybe once you get a pinecone and a yellowfeet; the next two times nothing, the fourth time a yew cone and two hazelnuts, next an apple core, etc. Or you could just make it something to pick up like beach trash, or stick it in stumps like this suggestion http://www.havenandhearth.com/forum/viewtopic.php?f=48&t=68375&p=859276&hilit=squirrel#p859276.
I would make it available in various forest/woodland terrains in winter on non-snow tiles and in spring.
I don't think it needs a penalty, but you could give a chance of a squirrel appearing and giving you 1-2 knicks and knacks before running off. Squirrel fever not required.