An observation: walk speed hasn´t increased at all, for horses it has decreased relative to MTW. Run speed has increased significantly, though it is worth to make a little comparison. A normal walk speed for infantry would be about 5 km/h, while trained men should be able to run with 20 km/h, so it wouldn´t be implausible if men run 4 times as fast as they walk, of course we have to consider that they carry armour and that would probably reduce the difference. But for normal inf units we have in RTWdemo a ratio run to walk of 2.5. That´s surely not an unrealistic fast run speed. For horses it´s rather unlikely that a canter and even more carriere are only 4 times as fast as walk, so they should rather be quicker.
Of course, the question is whether the walk speed is realistic, but if it isn´t, it has been so in MTW.