Is Arvak Better Than Shadowmere?

Tl:dr, Arvak is a very convenient horse but Shadowmere is a very useful house. ... That said, I think Shadowmere is the better overall choice for people who want more than just a horse (it's not thaaat much harder to just constantly steal houses if you just want a mount after all).

Is Arvak the best horse in Skyrim?

Arvak is the best, because he doesn't do any of the stupid stuff that other horses do, like run off during a dragon attack, blow your cover by attacking bandits, go missing, or die. Plus, he is available whenever and wherever you need him, as long as you can summon him.

Does Shadowmere disappeared after Arvak?

If you interact with other horse while using Shadowmere he is "deactivated" and goes back to his pond. He can disappear for good on some occasions as well. Probably going to the Soul Cairn and/or doing Arvak's quest seems to make him vanish, too.