9-5 on their website

Since they have to hike in their supplies they would require little to no snow, so it would be closed.

Roughly 1200 feet or 365m. It starts off very easily and is completely flat until you get past the lake. The trail is well maintained and is manageable by most people. Once at the teahouse and you've had tea and cakes, consider going the extra mile or so to the glacier lookout point, provided the weather allows.

Its open only in the summer months i believe. The family that owns and runs it told me that when we were up there earlier this month. Btw there are 2 tea houses. The above is for the 6 Glaciers. I dont know about the tea house at lake Agnes, that may be open till later as its closer to the hotel.