I just came back from hiking up to Emerald lake with the family (youngest son is 7). It is packed snow all the way up so definitely doable without snowshoes - we just had hiking boots. I would recommend gators if you have them, but the kids managed fine without - just got wet feet. It's doable in trainers, but you'll get wet feet and it will be slippery on the steeper parts.
The lakes are all frozen and mostly covered with snow, so not a pretty as in the summer, but the scenery is nice and we all really enjoyed the hike. Dream lake has some blue ice showing (first photo below) and was pretty.
The only 'tricky' part was finding the trail from Nymph lake. You cross the lake and follow the trail up to the left, but there are multiple trails that petered out. We ended up hiking up through some deeper snow on a slope and found the main trail. Basically though if you hike up to the left on the far side of Nymph, you should hit the main trail to Dream and Emerald lakes.
The Alluvial fan area was also interesting. Although the road is washed out in a spot, you can still hike down it and around the area.
We didn't hike around Moraine Park, but it didn't have much snow - looked to be more 'mud season' type hiking. Also saw lots of Elk.
A couple of relatively unprocessed shots, Dream lake and just off the trail near Emerald lake.

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