I have washed trainers in the washing machine and they have been fine. I would look to see how strong they are first, otherwise try soaking them in HOT water and biological powder overnight, this should clean them up a bit! :)
If you have the sheepskin variety I definitely wouldn't put them in the machine if I were you. Especially considering the cost of them!! Here is a link I found advising on how to clean your sheepskin boots.
If they are genuine UGGS no, no, no! You need to get the special cleaner from the manufacturers. It's a pain, and it's expensive but the washing machine is too aggressive for them and will ruin the sheepskin. One of the UGG type boots is made to be washed in the machine but definitely not the UGG Australia ones.