Thanks so much for the input everyone.
I tried out the approach I posted video of with a softer spray nozzle and longer lead, and it went reasonably well. She wasn't exactly happy with the process, but she would stand and let me spray her chest and legs for several seconds. I didn't want to stress her out too much (and my hand was giving out), so we stopped with that. This particular mini will 'explode' (rearing, bolting, etc) if under too much pressure, which I think is part of why this way worked with her. My other mini is more evasive (will swing her butt and kick first then move to rearing, etc) and a bit more suspicious generally. Will be interesting if the same way works with her, though she might respond better if I keep the water on her.
I technically have access to warm water. I have 2 barns...one where the horses are, and another that was used for other livestock. The one where the horses are does have warm water I can easily get to....but I don't have a small, safe fenced in area nearby. I do have that by the other barn, which is where I opted to bring her.
That wash rack is a great idea. Just need to figure out where I could put one.
I've stared working with them on tying, and so far its going well.
I wound up clipping them on sunday, since it was rainy. I'm glad I did, since it was in the high 60s today. Still in the 30s-40s at night, but I have blankets. They're both pretty good for that.