If I am under siege, I understand that caravans, immigrants and emissaries will not arrive. What will I miss if I maintain a long siege through a whole season? More especially, do any of those events happen during the winter?
Migrants do have a chance to come in any season, so I guess that would be your main worry. People dieing decreases the chances anyway though.
A goblin caravan might come if you happen to have friendly goblins around. However, given the likelihood that that's a goblin siege, they wouldn't be sending one anyway.
If it's a season other than winter, you won't get a caravan, but the liaison will arrive after the siege is over. (Goblins don't send a liaison, btw.)
The only thing that I can think of besides caravans and migrants would be crops, but there aren't any winter-specific crops, so you should be good there too.