If you were wanting to get some cow experience then there may be someone willing to let you do a bit of farm work in exchange for free labour. I'm thinking routine work like calving, feeding bucket reared calves, helping feed and bed cows or administer wormers etc.
If you can't have the cow(s) you've set your heart on maybe you could purchase some tame ones from a small holder or some baby calves to rear on milk. Have a look on websites such as Sell My Livestock to do research on prices, breeds etc. Otherwise there are plenty textbooks or references online to help you out. One that comes to mind is
https://www.fas.scot/downloads/ where you can find a free online Farm Management Handbook that provides costings. It's every farm consultants Bible.
Growing up we'd had a pet Jersey cow. She was truly more reliable than my shetland pony. I could decorate her in daisy chains, and take her for walks.
My current mare loves cows. I have a video of her being bathed (licked) by a heifer and she loved it.
If you can care for a horse, then you can easily handle cattle management. There is books and You Tube. It's just a case of learning new skills.