And perhaps the highest one without glaciers? I am assuming there are snowy peaks that do not have glaciers...

Colorado has 54 mountains that are over 14,000 ft. None of them have active glaciers on them and most of the snow that falls in the winter will melt off.

The highest peak in the Colorado Rockies (and the whole of the Rockies) is Mt. Elbert at 14,440 ft.

Mt. Whitney in California, the highest peak in the contiguous US also has no active glaciers on it and stands at 14,495 ft (or so).

So.maybe Whitney?

In the continental US, the highest peak is Mt. Whitney and it does not have any permanent snow fields or glaciers covering the peak - but it can snow on top any day of the year if the right weather comes in so be prepared at that elevation for any kind of weather.

Good Luck