Keeping horses and cows together?

Hi my family is thinking of getting a cow. And I was wondering if it is safe for both horses and cows to be kept together? My horse grew up with cows and calves, but I'm sort of scared the cow would pick on him or he would pick on the cow. Can horses and cows safely be kept together? Are there any diseases they can share?

My cows and horses have always been kept together. They can swap worms but as long as both are kept healthy there's really no harm
Typically the cows are afraid of the bossy horses and stay out of their way.
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I keep my horse in with about 12 heifers in the summer time but I don't in the winter because I don't want him to eat any of the corn that they get that time of year. He'll chase them around a little bit once in a while but for the most part they kind of segregate themselves and graze alone. I'm just careful about not putting him in with them if they are getting fermented feeds (corn, haylage or wrapped round bales). Also, alot of cow grains contain Rumensin which can kill your horse (or any monogastric animal) so keep that separated. Worms can be shared and also ringworm is fairly common. My horse got it from the heifers and it took soooo long for it to go away. I caught it from him as well. It's a fungus and it goes away when treated with Athlete's foot cream consistently but it looks disgusting and spreads like crazy. I'm sure your horse will enjoy his new friend :)

Ours are always together as well. Even our calves. I've gone out numerous times to find my cow horse letting the cows lick her from head to tail! So friend wise its usually okay as long as none have health issues

Our steer has grown up with my two horses. I was a bit worried about him getting playful and getting one of them with his horns but that hasn't happened. Though he still tries to play with them and annoy them the horses are the boss, he knows his place in their little herd since he has learnt to understand horse language.

The 80 acres across from me has horses and long horn cattle. Those cows move from the horses, as they have been 'taught' to doing roundups brandings etc.
One steer became a buddy of the older gelding.
The younger gelding had to come stay here for a while, as he was herding the calfs off the cows and would run them to death.