I lost Frost during the battle for Whiterun, was a shame I did like him. Shadowmere is good but not a patch on Arvok. You don't need to worry about him dying and needing to go back to where he respawns, you can just conjour him again.
except arvak is slower and dies right from beneath you so he's no help in combat. I only use Arvak if Shadowmere isn't around
Yes. There's a miscellaneous quest in Dawnguard where you can get a conjuration spell whereby you summon a skeletal ghost horse to be your steed. If he dies you can just summon him again. And he's called Arvak.
Arvak's summoning timer resets if you are still riding him. I can attest to this. That said, in terms of reliability and general not-annoying-the-f***-out-of-me-ness, Arvak is the best damn horse you could ask for.