Franz Josef glacier in NZ immediately came to mind, thanks to its low-elevation reach in a maritime climate.
Yes, there. The lowest parts of Fox and Franz Joseph Glaciers seldom have snowfall, even in winter, but the mountains above see a tremendous amount. It's enough to push the glaciers almost down almost to sea level.
Here are the other places I was thinking of:
The Atacama Desert is the driest desert in the world (though parts of Antarctica may be just as dry), but a few glaciers do exist (at least for now). Above 20,000 feet or so, it's cold enough that what (rare) snow does fall has formed glaciers over thousands of years.
Parts of northern Greenland see almost no snow (much of Greenland does see snow though), but it's too cold to melt what does fall, thus glaciers are formed.
Much of Antarctica is the same way. Most of Antarctica sees very little snow (the exceptions are in places near the coast along the Antarctic Peninsula). Since the temperature never reaches freezing in most places in Antarctica, glaciers have formed over millions of years of accumulation.
Another possible answer is parts of Mongolia, though summers are wet enough (all other seasons see almost no precipitation in much of the country) that it is a stretch to say that snow is seldom since summer does see snow on occasion in the areas where glaciers exist (the highest mountains of the Altai are actually wet by Mongolia standards-though still very dry [snow does fall in the Altai somewhat frequently], but some other areas in Mongolia with glaciers are much drier).
Coldest temperature thus far in 2018: -26 on 2/21
Warmest temperature thus far in 2018: 99 on 7/8 (All time record high)
Precip thus far in 2018: 7.89 inches
Snowfall thus far in 2018: 35.7 inches
Last frost of early summer: 7/1
First frost of late summer: 8/29
Last snow of late spring: 5/1
First snow of early fall: