Well the pool was starting to melt a few weeks ago and I do know we are going to have a lot of dirt, but that happens no matter what because we have a corn field behind our house. Our house is as dirty as the pool is...nothing good old rover can't clean out. We have such horrible water we looked at the snow and rain as a nice way to flush out some of the high TA and calcium. We may have a damaged liner sooner but I can't imagine it's any worse than a cover rubbing on it.
We were crystal clear last year (except for some kind of precipitate that we never figured out) upon opening. The dirt didn't come until the farmer started tilling!
This is only our second year opening, but the water looked clear from what was melting. I put in a huge amount of chlorine (I think I was at 25ppm) and we do put in the dreaded copper. I know it's not a bbb thing, and it may get us someday.
My sister's pool is a swamp, but they were already green in November before it froze. They open a swamp every year, but just toss in a ton of bleach and off they go to crystal clear water.
We only bought the cover to please our home owners association. I may speak too soon, but so far they didn't fine us for not putting it on. I never got a good answer from pool owners as to why I need to cover my pool.