first off welcome to the sight
next MY suggestion to you might be for you to get yourself a service manual on your machine to educate youself on your machine and what where and how things work on it
that said, your CHAIN cases I believe are located between each wheel behind the removable plate, and the chains in them should be in a OIL bath, as for what fluid to use in them(after you drain old fluid out)
well, that can be a loaded question of sorts, I an GUESSING that OEM< back in 1996, said to use 10w30 oil, or MAYBE gear oil in the 75w90 or likes weight
BUT since the fluids mostly ONLY job is to keep chains oiled, and lubed and from rusting, and MANY owners have used ALL sorts of fluids to do this, from NEW oil of many weights, and gear oils, hydraulic fluid, used motor oil, and so on
I don't think there is a 100% ONLY use this fluid type,
the thing I would maybe suggest is, just use a decent CLEAN , preferably new oil in a weight that works in your area's
as there really isn;'t any HEAT from the gears,a s skid steers move pretty much too slow for them to generate heat to cause any concerns IMO(and not saying I know it all or some expert) , but there isn't going to be any special fluid for heat protection from gears making friction heat build up, due to the slow goings of skid steers(unless maybe you drive them miles on end in a high two speed, which few folks do!
so as long as the fluid is clean and again workable in the temp range your machine lives in, all should realistically be good, not like your warranty will be voided , since this is a 1996 model! you just want your chains to be oiled with clean oil and water free!, its also a GOOD time to inspect chains and sprockets for wear and tension , when replacing chain case oil!, which would also be explained how to measure proper chain tension in a service manuals(good reason again to get yourself one, they can be found online, or places like ebay, facebook market place, in either real paper copies or downloadable file format) )
NEXT the dip sticks under the seat should be for gear boxes, some machines have a separate one for each side drive, some share one
I DON"T know your model well enough to say what your model has//
and as for fluid in these, I AGAIN GUESSING< but back in the 90's most I think took 80w90 gear oil, BUT might take 10w30 oil,
again your local JD dealer should be able to answer this with 100% correct type of oil used, or service manual again!
or doing a good online search too should net specific oil type and weight!
HOW to drain them, well, that again can be model specific, so, that service manual again would be handy! for you to have!
I personally like hard paper copies of them, and I stick them in a 3 ring binder and then use them to also log in PM"S with dates of them and what used/replaced and so on
good for keep track of things, as I get older memory isn;'t as good and things blur together too easy, I forget when and what on each machine, so paper service manuals get my vote there!
they tend to pay for themself over time, so I call them investments
they will also give you a time frame on when and how often to replace fluids like chain case and gear boxes and so on, , as water is the enemy on them IMO< condensation can get in them even in low use, I typically replace mine every 5 yrs or sooner, pending hours on them, , but use the 5 yr as a time frame even if low hours of use! to keep things rust free inside cases!
hope this helps some
MAYBE Others here might know exact fluid types for things too!