If the canes are still green, even under the soil line, then your minis are still alive. There is no reason to replace them. At the beginning of April (or, if you can find forsythia in your area, when that is is bloom), trim off anything dead, and start your fungicide spray. Even if there aren't any leaves, spray the canes. Keep up your spray according to the directions on the product. Blackspot treatment has to start before you see the disease, you want prevention/avoidance. If you wait until you see the spots, it is harder to treat.

Thank you, Diane. Yes, the canes are vividly green. Should I also remove the remaining mulch (most got scoured out by snow and wind) and replace it? And when should I prune the mini roses? They got rather overgrown and gangly looking, and need some neatening up.

Prune when the forsythia blooms. If you can't find any in your area (it is a yellow shrub that blooms in the spring), then early April should be fine for pruning.

I just put new mulch over the old.