I do a lot of re-enactment and I can say that the speeds they have coded in the mod are relative to reality. No matter what people think modern man is in no way SUPERIOR to those of the medieval era in a physical way. While yes, it does seem that they move quite slow whilst wearing linen but running with a sword is no easy task, nor with a giant wood and iron shield strapped to your forearm, especially when the majority of it is uphill. Ever had to fight up hill in a shield wall? It's not fun and is damn right frustrating sometimes. Speaking from personal experience here, these men did this day in day out, they were a lot more adept at anything we can do now, we are just simply not built for it by means of inconstant manual labour and a far superior quality of life. I'm a pretty big lad, I've done re-enactments for around 7 years now (Roman, Saxon and recently Pike block) and I can tell you after ten minutes of swinging that 5 lb sword around and holding that 8lb shield up you are pretty damn tired, no matter how fit you are. Adrenaline plays a big part of what we can and cannot achieve but adrenaline only takes you so far.
That said, horses back then would have not typically been faster. The counts and such would be riding destriers, a horse bred for combat, no speed. They were huge, hulking creatures designed through selective breeding to hold a man's weight and that of any armour and arms for extended periods of times. They were not built for speed. So, the horses in the mod are about right considering that the only horse breeds we have now a days are working breeds and those bred for racing. Destriers, palfreys and charges (and their respective sub-breeds) are all but bred out for their lack of need.
The speeds in this mod seem appropriate for the setting it is portraying, by my reckoning at least. I'm not saying I'm an expert, but from having personal experience in wearing the kind of kit they wore and partaking in (somewhat) the actions these men did and riding horses for a good portion of my life, the dev's have got it working well. Nothing needs tweaking.
Except maybe disallowing Pymous a crossbow.
Hope that helps to shed some light on the situation.