Theres a difference between running and sprinting, especially with mud soaked suits and carrying small supplies and those metal and wood sticks that bullets come out of, also the gear wasnt strapped to you in nine places, it bounced around a bit. In my opinion the soldiers who have backpacks and shovels and other gear hanging from them should be slowed a bit. Having to carry a four foot long rifle along with grenades a shovel and some supplies while sprinting would take a lot out of you even if you were trained but running slightly slower would cause you the loss of energy shown in RO2.
Well there's bit of problems here if we're honest.
1. Mud doesn't soak that well into wool clothing. It's actually incredibly tricky trying to get wool clothing dirty in the real meaning of the word. Water is slightly different story but even that takes a while before it genuinely starts too get heavy + there's no rain in RO2 so far and only drips of water you can find are pretty much just some very small "ponds" that barely rises above ankle-level.
Snow is also pretty poor example as what happens when you put wool clothing in contact with snow is usually it just "sticsk" into it and falls off as easily once you brush it slightly. It won't melt and soak in similiar way as with some other clothing.
2. Gear not being strapped is bit weird thing to note, as the key difference when it comes to gear slowing you down other than a very small amount is heavily dependant on how well you have adjusted your belt, as you want to keep it as concentrated "on" your torso as well as possible so it won't create any drag, but is more like balanced around your body as it is part of your body. Standard field gear + ammo (for a typical soldier) rarely exceeds more than 10-13 pounds for average soldier, anything more specialised might become bit tricky. Rifles also tend to be fairly balanced weapons despite their weight so carrying one on your arms has neglible impact. Submachinegun woudl be another story already for the sake of balancing, as PPSh with drums tends to be nose heavy. It does actually create a bit of drag, just very minimal one. AT rifle\LMG also is a drag in some ways. You could probably run faster with ~40 pound (smallish) stone in your arms than say MG34 because the shape and other obvious factors makes it more trickier to carry while trying to move fast.
(Here's more interesting example: You could easily carry two PPShs with you while being capable of running pretty fast as long as you put one on each shoulder, cross the straps and set them tight. Slight slowdown in speed but obviously that would be impractical as hell if you would try to crawl or so. Additional ammo would also become an issue but this is purely for sake of being able to do something and how it influences some things.
Also with typical soldiers I mean non-MG'ers and engineers for the most part, but then again MG running speed is quite reasonable in general.)
3. The differences between german and russian average field gear for standard loadouts is... well, interesting. Russians have extremely minimal extra to slow or even drag them down, germans have also the same thing for the most part. The so-called A-frame and your gask mask container won't really cause major issues as long as you setup your belt and such right, aka tight.
4. This is authencity quirk, but generally speaking if soldiers are prepared for extended combats only the absolutely necessary eguipment will be brought with you. Any unnecessary carriers, holders or so are disrcarded; you can always tuck your e-tool in your belt in certain angle it wont' be in way of movement but you can very quickly pull it out and use it if necessary. Especially for urban warfare one could note the germans are "overeguipped" in RO2, but only by certain standards.
Running speed in stairs could be toned down somewhat and possibly the stamina recover rate, but the baseline speed for running is not really as silly as it would sound like in some ways.