I do not feel completely guilty about that as I had called the rangers' station twice before our trip to ask about backpacking permits and trail conditions. The first time I called I was advised to bring snowshoes, the second time I was told they would not be necessary. I am so grateful that we decided to bring snowshoes with us! Without them we would not be able to hike for even few hundred meters. And even with snowshoes it was a too big challenge to go on the hike that we had planned. We had already lots of trouble following the snow-covered car road that was leading to the trailhead of our hike. Trying to find a narrower hikers path would inevitably lead to us getting lost in the middle of the forest.
Because of that we had to abandon our original plan and flee to lower elevations. This is how we ended up in Yosemite NP, even though I had expected it to be overcrowded...
This road sign was at the end of the car road, just before the trailhead of our planned hike. As you can see, it was almost neck-high covered in snow:
Pretty Woods Creek that we followed for a while in our snowshoes:
All in all, we do not regret going to Mokelumne Wilderness and for sure we will go back there in future. If you also plan to visit it, I would say do not go there before mid of July. And do not rely on the park rangers for information, they seem to be useless (Both times that I called they also "forgot" to mention that their office is closed on weekends, and therefore, I would not be able to pick up the backpacking permit from them and I should had it sent to me by regular mail...).