Yes it does depend on the cow. That said, I usually bring the cow in to the calvesfor a week or two and once her milk has gone through them, they smell right to her and she usually will take them. If she has her own calf plus some others, they will learn quick to go nurse her when her calf goes on her.
Just had a jer/hol cross heifer calve. Got 2 more holsteins to put on her, 4 days later. She let them nurse from the first as long as she was eating grain. Knocked them off the first 2 days after the grain was done, now is tolerating them pretty well. I'm leaving her in the pen all day with them and she isn't bothering them too much, then turning her out at night. By next week I am sure she will be okay with them. I just want them up and real active when they go out so they will stick with her calf and follow right along.
Most holstein cows make alot of milk and can scour calves if you don't have enough. Used to put 6 on my one 3/4 holstein. Put 4 on her, then pulled 2 off and put 2 more in there and made sure they all got enough...started leaving her with them for 6-8 hours a day and they were learning to go and get a little, watched that none got scours or looked like they were being shortchanged. After about 2+ weeks, they were all looking good and they went out with her. She was always milked out and they all grew but that was an extremely good cow.