We are trying to find the cause of the unit to fost/freeze solid on the outside. I still heats. Will it cause more problems if we leave it running?
We have had a repairman over 2 times, but he cannot pinpoint the problem.

If we're talking about a heat pump that is icing up then, no, running it could cause damage.

If the unit is frosted/freezing over outside without going into defrost every once in a while it is not heating but the second stage electric or gas unit is doing all the heating. Now this is based on the fact that you have a heat pump but you did not mention that in your post.

Yep