I'm not sure it does feel somewhat random. It seems the higher the haul skill is trained the more often they will haul and certain animals seem to haul more often. Huskies seem to me to haul more often than labs or boars for instance.
I do know that after getting 6 huskies bred and trained for hauling I don't need to haul anything too often anymore.
I do know that after getting 6 huskies bred and trained for hauling I don't need to haul anything too often anymore.