To answer your question, No, you can not retrieve a downed animal on private property without the landowners consent. Yes, the landowner could take your deer if it is on his property if he or she so chooses...it happens all the time. Retrieval of game is no excuse for trespassing!

If it happens, tell the landowner what happened and I bet most times, he/she will grant permission to retreive your kill.

This is the law in Wisconsin...I can' t speak for other states