OK< My 2 cents here, when you say you get stuck, are you getting stuck due to tires packing and then loosing traction, or are you sinking into the ground and getting hung up from dirt getting under machine and then lifting tires off ground enough to loose traction?
as there two different types of stuck
and each can be solved differently(or the same way maybe)
First if your getting stuck due to machine sinking and thus high centering things(lifting wheels up and not enough down force on them then for traction) then what you most likely need to do is, wait longer for the ground itself to dry and not be holding so much liquid, that its causing the weight of the machine to sink and lift its tires
its just gravity at work, and not way to beat it till its drier and harder ground
BUT|, there are ways to make a skid steer stay on top better and get it to work in and on softer ground,
the most common will be adding tracks,
and that is adding Over The Tire Tracks, this then makes the machine have less ground pressure and gives it more ability to float like on top of softer ground, it also then creates a larger foot print with more of the track in contact with the ground, so that gives it more traction
these tracks can be had in both metal and rubber versions, neither is very cheap, and both have pro's and con's
some machines need to have spacers added to allow for clearance of over the tire tracks,
adding tracks can also add more stress to the machine and its drive train, they will also, rob machine of some HP
metal tracks, IMO work the best in very soft and muddy terrain, , and I think tend to be the cheapest to add!
but they can be hard on the ground there used on, as in can damage pavement, concrete, and like surfaces that can end up costing to $$ to repair on a job site
rubber tracks, will for sure enable a machine to go more places than tires, as they again cause a much lower ground pressure, offer way more track contact with ground for more traction , and do way less damage to the ground there driven on
they typically cost more, wear faster(well pending surface used on) BUT they offer less traction in very sticky mud, as the lugs can fill up just like tires do, causing them to get smooth and slick(metal can also, but they stay clean longer IMO)
the biggest draw back might be to tracks, is, they will allow you to take a machine into places it would NOT go on tires alone, SO< in other words when you get stuck with tracks over tires, you might end up in a spot harder to rescue the machine , or need larger equipment to get them out as once them larger foot prints sink, they cause more suction than just tires alone(or again in MY experience)
SO< YES they 100% get you more traction and flotation, but when you get one stuck they can be harder top get out than tires? NOT all times, but IMO more than tires alone
NEXT as for getting stuck due to tires filling up with mud/dirt!
they sell tires of all shapes and sizes and thread designs and thread depth , the deeper the threads the longer it normally takes for them to pack up,
so if your current tires are worn down a lot, new tires might be an option here for you, and MUD designed tires at that
pending SIZE of tires on your machine,, you MIGHT be able to go to a larger wider tire, this MAY require the use of wheel spacers for them to fit and work,, every machine is different here so, there is no way for me to say THIS SIZE to get!
NEXT is, and this gets more into custom making, but for yrs, some folks have actually added DUEL wheels to machines for better mud work
its not super common, and takes maybe doing a bunch of online searching to find some pre made, or having them custom made for YOUR machine and spec's
but adding duel wheels to all 4 corners, can for sure get you more flotation and traction, just like tracks do!
and they will also have the same negative effects, of adding more stress to the drive train on your machine,
but it is an option, so I added it
NOW for maybe some cheaper optiions, for stuck typs of just the tires filling up with mud, and thus you loosing traction
is, adding come HD tire chains, typically most use these for snow/ice work
BUT they will also add a bunch of traction in mud too
BUT to be honest if your mud has NO bottom and your sinking in and getting high centered, chains ain't going to help much if at all
as chains, need something to BITE into to help give traction,
if the mud is just soft and deep with no rocks or base to the bottom, the chains will not help much as there not getting anything to land on to push off of,
and just like tire threads, they will soon get covered over and be almost a smooth tire looking mess!
chains do off stress to drive train too, but as long as on soft ground, its the least of things , but they will also damage certain terrain, from grass, pavement to concrete and so on
SO< those are basically the ways to work in muddy condition
, and even these have limits
it all comes down to the type of ground/mud, and machine set up as to how far or well it will get by and again no 100% rule to go by!
cheapest option typically is waiting for drier conditions but its not always optional
lastly, if your running a machine in very muddy condition, you also need to be cleaning it way more often, and this includes cleaning out the belly pan on BOTH sides, oil coolers, radiators and so on, if not you could be shorting the life span on your machine by a LOT, or risk a fire or other issues!
mud packs up and can be powerful stuff damaging things!
also should be greasing things more often too!
hope this helps