Do horses and cows interact

NO! If you put a cow with a herd of horses that poor cow is going to be harrassed 24/7, unable to eat, sleep or even get away from these aggressive, bossy creatures. Horses tend to jealously guard their feed stations (especially if you have only one feed station to share between the animals), nipping, kicking and biting any other creature, be it a cow or llama or goat, that comes near to "steal" their food. If you are going to put a cow in with a herd of horses, make sure you find some way to feed her separately from the others, so that she gets her share and the horses don't steal it from her. If that is a problem, then it will be in the best interest of your cow to have her in a separate corral or pasture from the other horses. In her own corral she can eat whatever she likes in peace and sleep wherever she wishes.

It is alright to have horses and cows together if the cattle outnumber the horses (like if you have 1 or 2 horses in a herd of 30 or more cattle). This way the horses have a little harder time to keep their feed stations to themselves, and with more animals you have to feed more bales, which, in turn, means more opportunity for the cattle to eat their bale in peace without having to worry (much...) about getting kicked off their bale.