There are many mini breeds of cattle - Zebu, Dexter, Scottish Highland.... and there are "mini" versions of Herefords, Angus and Jersey to name a few. But *sometimes* the minis can be much more expensive than the full size cattle breeds. But they are generally calmer, and easier to house and feed due to their size.
Our family raised Herefords for close to 100 years before selling the herd and downsizing to Dexters. The cattle that had only known cattle really freaked when I moved my horses to their pasture. So you'll probably want to make any introduction of a new species a slow process. On the flip side, my "pet" Hereford that was bottle fed and raised with my horses and NOT cattle, freaked when I tried to put her out with the cattle. I tried for months, and she would never bond with them, so she lived with my horses her entire life.
If you just go slow, you might find the cow adjusts to whatever you introduce her to. BUT!!!! Keep in mind if she truly is a COW (or heifer - cows aren't cows until they freshen), and is a female bovine, and not a steer, she WILL go into heat on a regular schedule. And SHE WILL try to mount whatever she feels attracted to. Horses, goats, dogs, wheelbarrows, humans... I've seen it all. It can be a major problem if the "mountee" is smaller than the "mounter". You can damage backs and hips.... So keep that in mind. If all else fails, you may need to seperate the in-heat animal for a few days, until the mounting urge passes.