An army suffers from non-combat losses. There is a 10% chance each time you move from one fief to another that you will lose men to attrition. There is also a chance of attrition for any days you have left at the end of the season.
Attrition can wipe out your entire army if you enter a low population fief with a large army (i.e. over 60,000 troops). Armies had to live off the land in these times and the troops would simply drift away if things got rough. Battles are easy, starvation is hard. Attrition rate varies by season with winter and spring harshest.