Ice climbing ropes

So I just picked up the Trango Diamond in 9.4 and realized that it is only "sheath dry" vs being "duo dry". I have no intentions of taking this particular rope on any long alpine routes or anything, but will it be suitable for just going and climbing on ice for a few hours? Or because the core is not dry treated as well, will it freeze up super quickly? Any input is appreciated!

It's fine.

I've used that same rope for 2 winters now and am very pleased with it. It stays drier than Petzl's top-of-the-line Arial rope.