Yep, I have the TOTD ones (in burgundy!!! ;)) and I wash them in my machine all the time. Regular cycle, with saddle pads and other wraps and whatever else finds it’s way in…they’re holding up great!
My TOTD boots died from washing, the elastic all stretched out. They are decent for the price, however, and definitely much better than the Dover cheapies.
My favorites of all time, though are the N.E.W. dressage protection boots. Light weight, easy to wash, no elastic, very nice fleece. Unfortunately you almost never see them in the US anymore, but you can order them from AmiraEqui in the UK.