I was skeptical about carpets at first, but discovered something. Have any of you see the traps with upward facing dispensers hidden by snow? Carpets work better because they're both thinner, more natural to have in a place you care about, and you can't right-click the dispensers through them.
Edit: To tame horses, you must keep mounting them until they don't throw you off. You can speed this up by giving them apples and sugar. When they accept you, get off and put a horse saddle on them. From then on, they'll be under your full control. You can give them different forms of armor. Something significant is, while on a horse, the exp bar is replaced by a charge bar. Hold jump and wait for the bar to hit the yellow spot to jump higher.
Leashes can be used on any passive mob, as well as multiple mobs at a time. I brought a horse and cow into a lava pit with them. Finally, a definite way to bring mobs with you. Hay bales seem to not have a use yet, and don't even burn when lit on fire.