How the quagmire conditions vary with weather depends on the nature of the muck.
For example, if we get a lot of wet weather, then my Harris Creek slide silt becomes more saturated with water running through the ground, resulting in more and softer quicksilt to sink into!

But for my other bogs, it means high water, which keeps the mud submerged even further underwater.

If rivers run high, mud and quicksand tends to be submerged, although the rapid flow of water is also at work, moving mud and sand and clay around and depositing it loosely, creating fresh areas of mud and quicksand under the water, waiting for drier weather to drop water levels to expose it!
If we get a lot of dry weather, then my Harris Creek slide area dries out, reducing the number of places where the soft stuff is close enough to the surface for me to activate it to very few, and perhaps eventually none.

But, that also drops the water levels of lakes, ponds, streams and rivers, exposing the quicksand and mud along river banks, as well as the parts of the muddy bottoms of lakes and ponds beyond the inside edge of the shoreline grass, stuff which range from shallow to bottomless!

You won't know until you check it out!
But, too much dry weather can result in the loss of any nearby cleaning areas (places that you can get to and from without risking being seen by anyone), surrounding the water usually used for cleanup with a margin of more soft mud, preventing you from getting from the cleanup water to solid ground without getting muddy all over again. Or, the cleanup water can be gone altogether, with the cleanup pond being one huge mudpit. But, if you want to sink into those places badly enough, you may have to haul buckets of water from somewhere else to use to clean up with, which may be a bit of work.
Depending on the size and depth of the sinking areas, the mud may even dry out as well, although deeper ponds and lakes may have the mud turning firm a little ways out from loss of moisture, but still remaining soft closer to the water, where it is more freshly exposed. In fact, you may then find a wide range of softness to enjoy, with it being extremely thick and doughy closer to shore (most stimulating), becoming progressively looser the closer you get to the water, in some cases allowing you to swim through it in the really loose stuff!

But, as Nessie already mentioned, when water levels rise back up, the mud doesn't loosen up as readily, resulting in water on top of stiffer, compressed mud. It can take a long time, or perhaps until the following spring, for it to become soft again. Buildup of swamp gas does help with the loosening, as does freezing/thawing.
I have a sinking spot where I help it along by loosening it while it is still underwater, turning it into a nice soft patch of undulating ooze, with the depth of the softest part being the limit to where I had loosened it, with stiffer mud below that. It then gets thicker and thicker through the season, until I can sometimes walk on top of it at the end of the season, or take half an hour to work myself under it because it is so thick. Then, the following spring, I have to loosen it all over again, while it is submerged underwater.