In 2007 on June 11th and there were a few patches of snow around the ridge and what not but there was none on top. Usually the way snow works around Philmont is by that time in June there's some snow in areas that don't get much sunlight, but out in the open like on top of a peak it's usually all gone.
It's possible if there was a major snow storm right before the season started that there could be snow on top, but I think it would have to be pretty serious to be enough to close the peak down to trekkers.