I have a mule and cows, and a mule is half ass:smiley-laughing013:, so here's my opinion....
We had a heifer first. She was here for 1 year before we bought our mule. It was the end of winter, so both were in the barn for 2-3 months before they were turned out together. They were stalled next to, but not touching each other. And they were the same age (although, like I said, Millie was already here for a year).
Penny the mule and Millie the cow got along great! They would put on their own rodeo and run and kick up their heels chasing each other. Penny would give Millie a kick every once in awhile.
We had Millie AI'd, but unfortunately she died at 5 months gestation.
We bought 3 holstein bull calves 2 months later. They were so little and Penny is used to playing ROUGH - so we put off introductions until this year (although all winter they could touch noses in the barn). It went well at first, until Penny decided to try out her old games on the new cows. 2 ignore her - one freaks out and repeatedly runs thru the hot 4 strand electric fence.
We also have 4 goats, and Penny will play with them, but they know the game and will play by her rules!
A farrier I know has a john mule that he says he would trust with nothing smaller than him. He's tried to kill calves, goats, etc.
Long story short: I would be leary of an untested jack with a pregnant cow.
