I use clicker training with my two horses and am officially sold!
I don't use a clicker for the same reason Katie mentioned, I just use a 'smooch' sound I make myself. The click is simply the bridge it means 'yes you did what I want' you can do it whenever they do something you want and that buys you time to get the treat. :)
As for how to teach tricks, such as those things you mentioned AND agility, I use clicker training.
Here's how I do it:
Always in short 5-10 minute sessions to begin with, you can do multiple a day. The break gives the horse time to calm down off the excitement of food as well as giving them time to think about exactly what they needed to do to get the treat. Next time you go back they'll be so much faster with whatever you last worked on. I use 1-2 large carrots cut into tiny pieces, gives me about 10 minutes worth of treats. You could also use Celery or anything else your horse likes.
I start by teaching them how to take a treat respectfully, as 'mugging' is a big problem with hand-fed horses. If the horse is respectful I'll do this in their stall, if they're rude I'll stand on the outside of their door where they can't reach. I stand with the bucket of treats, they know it. They'll start by sniffing you and mugging you and trying to get the treats, stand calmly, move away a little if they get mouthy and just generally ignore them. Then the moment they look away, for anything (Even if they get distracted) make you click sound (either with a clicker, a smooch, a cluck, whatever it just means 'yes') and give them the treat arms length away. If they're rude about hand feeding use a feed pan in your hand or on the ground in front of them. Repeat this until they are actively moving their head away from you to get the treat. Don't build a bridge by waiting for them to nudge you then turn away, but sometimes click and treat before they come back to you. Sometimes feed them the treat right in front of their chest meaning they'll have to lean or step back to get it. This helps maintain you're respectful distance. Repeat this for a few sessions, it took my pony 2 and my draft mare 6 sessions in order to get the concept and be consistently respectful.
The next 'trick' I teach is target, as you can use it to teach pretty much anything, backing, following, jumping, going through the obstacles, playing fetch, bowing, everything!
I use a crop with some brightly colored duct tape on the end because my mare had trouble seeing the black tab at the end. I hold it out and wait, my pony was immediately sniffing it. The moment his nose touched I clicked and treated. Repeated this 2-3 sessions and he was following the crop all over his stall and touching it high up and low down and backing up to get it. My draft mare was afraid of the crop, from a previous owner. So I actually had to put a treat on it, she got it fast :P Then I just worked on when she touches it with her nose she got her click + treat.
I'm working on teaching them to stand on mats, by targeting with their feet. My pony has learned to target a football, we're working on fetch but he'd rather kick it than pick it up :P My mare has used her following the crop skill to overcome her overwhelming fear of going new places. She has sense learned about cars by targetting the crop on my car, any scary object gets made into a game! A friend who does the same can get her pony to load herself on a trailer by putting the target in the trailer!
Here are some videos I used to learn how: Video 1
Good luck! keep up posted on what your horse learns, we'd love pictures too!