Going up out of Happy Isles, the only trail presently open starts up the John Muir Trail, then crosses over to the Mist Trail above Vernal Falls and ascends from there. I don't know where the snow line currently is on that route.
On the south side of things, the snow level is much lower, as explained below. The Four Mile Trail is closed for the indefinite future. There is a chute near the top, which the trail crosses, that is normally full of icy snow until well after they can plow the road to Glacier Point. Which won't be any time soon. They won't open the Four Mile Trail until after that chute melts out.
So, what to do when you are tired of the rather limited trails around the valley? Well, first make sure that you have found them all. The Park Service is always trying to minimize the number of trails. Their phase one is to take down the trail entrance signs. After the traffic dies down in a few years, phase two is to stop cutting the dead trees that fall across the road and to stop maintaining the culverts and bridges. Eventually, phase three is to deny that there ever was a trail there, as they do for the Sierra Point Trail, the Ledges Trail, and the Indian Canyon Trail.
Here are two very easy trails that we did last week with my five-year-old granddaughter. The first is the trail along the river from Happy Isles to the entrance of Lower Pines Campground, then on to the Awhanee. Start by crossing the bridge at Happy Isles to get to the north side of the creek, and start walking downstream along the bank. Almost immediately you will find the old pavement, which extends the rest of the way, though in some places it is beneath some sand and pine needles. This trail is at phase one, mentioned above, and is in excellent shape. I think that they took down the signs because when the river is at maximum flood it can go under water. The creeks and waterfalls are in full Spring runoff, but they are not at flood right now. If the trail is dry, it's OK. If it's under water, please have enough sense to stay out of the river...
When you get to Lower Pines Campground, go in the entrance, and follow along the right hand road until you see a "fifteen minute parking" sign near the bank of the creek, which comes out of Tenaya Canyon. Walk along the bank for a short distance until you see a foot bridge over the creek, which puts you on the north bank of the combined creeks. From there, cross the (currently closed) backpackers campground toward the Royal Arches cliff, and you will immediately see the paved bike trail to the Awhanee, where you can pick up the shuttle bus. The Awhanee itself is worth a look around inside.
On Tuesday afternoon, we did a nice easy hike that starts at the "Discovery View" parking lot at the east entrance to the Wawona tunnel on route 41. This is the trailhead for the Pohono Trail, which runs along the valley rim all the way to Glacier Point. But you aren't going there, just 0.6 miles to where it crosses the old Wawona road. This was a main entrance to the valley before the tunnel was built. Since then, it has been a trail with great views, that goes to the base of Bridalveil Falls. However, it it now in phase two of abandonment: The culverts are gone and there are numerous fallen trees across the trail. None of the trees present any real obstacle, however, since you can just walk under or around them. The two stream crossing, however, could be a problem in very high water. Fortunately, even in Spring runoff these creeks aren't very big. In fact, the road never had any bridges in this section, just a couple of culverts that are now gone.
Old Wawona Road and Silver Strand Falls (on Meadow Brook) as seen from the hike
View from Artist Point
Artist Point is not a real point, but just a place on the road with great views, just before it crosses Artist Creek. This had a couple of logs across it, where the five-year-old needed a steadying hand to avoid stepping in the creek. Which was about four inches deep in most places.
Further on, you cross Meadow Brook, which has a lot more water, but is wide and not very deep. The easier crossings are up the hill a hundred feet or so, but we just walked across on a snow bridge:
Meadow Brook crossing, looking back
Snow bridge across meadow brook; Ribbon Falls and El Cap Gully from that point.
Here are the details: From the tunnel parking lot, it's 0.6 miles and 500 vertical feet to the junction with the old road. It's 2 miles along the old road to Bridalveil Falls, of which the last quarter mile is on the shoulder of the new road. We also hiked up from the junction about 0.25 miles to get the view from Inspiration Point. It may not be the official viewpoint, but the view is pretty good, and above there the trail runs into the woods and was covered with snow. The snow is not very deep, but in the morning you can't dent it all all without spikes on your shoes. In the afternoon the surface could be marked by an adult, and steps kicked to a depth of an inch or so, but it was still slippery and the kid left no imprint at all. You had to hold her hand, or she'd be over the side in a moment.
So, the snow level on the shady side of the valley was at about 5200 feet last week, or roughly a thousand feet above the valley floor. Looking over at the sunny side, the snow level was up at the valley rim.
Another easy and seldom done hike is on the sunny side of the valley: the Old Big Oak Flat road, which is well described in this posting: Old Big Oak Flat Road hike
It is in much poorer shape that the one we did last week.