Ok, so I was wrong. There is one lake in Naturalist Basin that was fully free of ice: East Morat. All the rest were at least half frozen. The next closest to being ice free was Faxon Lake, which appeared to be about a 3rd frozen. The rest were all fully frozen, or at least 75% frozen.
So
@Skiwi, here's a mini report with answers to some of your questions that may help you decide between Middle Basin, Naturalist Basin, or elsewhere for your trip this weekend...
The trail from Highline Trailhead to the final turn-off from the Highline trail is pretty good save a number of small stretches where it does get a bit wet and muddy, but there are plenty of rocks to step across and keep the bulk of your shoes dry. There are well over a dozen tree falls across the trail. A few were low enough to just step up and over. Most, however, required a good detour off trail to get around.
One of the many tree falls.
There are lots of little wild flowers that have popped up along the lower trail.
After the turn-off from the Highline trail, the trail really starts to get get wet, that is, it really starts to go underwater at some sections.

Somewhere under that water is the trail. Fortunately it can all be bypassed by going off trail.
Soon after these wet sections you reach the fork where you can left and on up to Morat Lakes and the western side of the basin, or take a right and head up for Jordan Lake and the eastern side of the basin. If you choose Jordan, you'll have to forward the creek right after the fork, and the creek is running pretty high from all the snowmelt right now.

You can see above that the trail runs right through the creek where the rocks are all lined up in a row. The water appeared to be at least knee high and possibly even waist high right in the middle.
After seeing that, I opted to go back and take the route up to Morat Lakes where I set up camp for the night.
Early in the morning, I made my way on up to the upper bench where Blue Lake lied. It was completely frozen over. I then worked my way up to the ridge that divides Naturalist from Middle Basin.
You can see there is still lots of snow in the upper edges of Middle Basin. Agassiz is on the left and Hayden Peak to the right.
A zoom in on Ryder Lake (middle) and McPheters Lake (upper right). These two and their surrounding sibling lakes all still appear to be mostly frozen over.
A look back down into Naturalist Basin from the ridge.

Still lots of snow across the upper benches. I post-holed through a great deal of it to make the rounds to each of the lakes after descending the ridge.
Zoom in of LeConte Lake (lower left) and Jordan Lake (middle-right).

The edges on each lake are just barely revealing liquid.
A close-up of Jordan.
Making my way back down to Morat Lakes. The left one (eastern Morat) is the only lake in the basin that was without any ice.
Mosquitos were not bothersome for me at all. I brought some repellant and a bug net for my head, just in case, but was never bothered enough to get out either.
All in all, Naturalist Basin is doable with no special gear, as I was able to do, but as you've now seen, conditions are still pretty wet and mushy up there with some significant snow drifts and what not still in process of melting out. I did take some spikes along which I used to help me up to the ridge. If you want to explore the upper bench, you'll be post holding. You'll also be getting your shoes and feet wet, no matter what. I lost the trail a few times on my way up to Morat Lakes due to snow and run-off, and had to pull out my map a couple times to find my way back to it.
So, you could still do Naturalist, but, depending on who you have in your group and what your objectives are, you may have a more enjoyable time somewhere a little lower. When I signed the register, there was only one other party signed in, and they had gone up to Four Lakes Basin. I did not see a soul on the trail going up last night, nor on the way back until I was about 1-2 miles shy of the Highline Trailhead again. At that point, another couple were on their way out to Four Lakes Basin. So, Four Lakes Basin seems to be a good destination of choice right now that you may want to consider instead for this time of year.