It depends...was that part supposed to be on Vvardenfell or mainland Morrowind? Horses could probably survive on the mainland at the time, and there's no reason to assume Vivec wouldn't ride a horse if he had access to one. Why make things any harder on yourself than you have to? Even a God probably prefers to do things the easy way.
edit: The part I personally find hard to believe is Vivec wearing fine robes. He never wore much more than a loin cloth and a few pieces of random armor when I saw him. It seems like being a God in the Elder Scrolls mythos causes one to become progressively more naked as time goes by. The entire Tribunal were pretty much letting it all hang out when we meet them (even Sotha Sil, or especially so. He appeared to be completely naked. That wasn't armor, it was his metallic body!) and half the Daedric Princes are pretty much half naked.
Also, the description of him as a "tall Dunmer" made me laugh. He wasn't all that tall, and he didn't look much like a Dunmer.
Think Dr. Manhattan from watchmen. The more detatched from his former humanity/mortality he becomes, the less importance he gives to clothes and other human distinctions.
Personally, I like to think of it this way. Whether or not you buy into Vivec's claims that his mortal and divine beings were only the same for "one red moment," the mortal Vivec needed some motivation to kill his king and liege-lord, correct? So whether or not Vehk the God killed nerevar, whether or not he is the same person as vehk the Mortal, and whether or not their motivations are different, the best motive, both from a logical and rule of cool standpoint, is that Vehk the Mortal wanted Almalexia the Mortal in the sack and so they betrayed and killed Nerevar. The rest was just gravy.