there are some quest that, while active, disable teleportation to prevent you from teleporting. There's one where you have to unblock the teleport locations. perhaps you should look at your active quests and finish the ones that could be causing this. This appears to have been the problem; I still ...

I've tried teleporting and summoning my horse in various outside locations, but nothing happens and I get the message.

God mode is disabled. No luck.

In game, I can't use any teleport spells, nor can I use my Horse Whistle. If I try to teleport, or use the whistle, I get a "This is not possible at the moment" message. I have plenty of teleport runes and my horse is still alive. I've tried restarting the game and tried using the teleport spells in...