[silly me, I took so long writing this and getting logged back in that my response is now redundant -- oh well...]
Hey Marie,
For training level, pneumatic tires and wire-spoked wheels are allowed at Happs and, I believe, the other northwest CDEs. You'll DEFINITELY want No Mor Flats innertubes or slime-filled tires, and be forewarned that the Happs marathon course is quite rough in an easy entry cart (ask me how I know...).
They no longer requires a spares kit, but you'll need to carry a few things anyway, especially a halter and lead rope.
A great resource for beginners (and beyond) is minihorsecde.com. It covers all the basic questions (such as those you asked) and includes a conditioning program that I found very helpful. :modedit: (links that go to interactive mini horse forums other than LB are not allowed) Leia and Amy's past posts on LB about their CDE experiences will give you a ton of information.
The Happs website has oodles of information, including the particulars for each event. Maureen Harkcom, who runs everything, is unbelievably helpful -- even in the midst of running everything, she took the time to talk with me and introduce me to someone to shadow for the day (Terri Jones).
You, Vicky and Erin need to come up for the Happs CDE in June...just being there is an education -- not to mention a total blast.
The assorted schooling CDEs at Happs are a great way to test the waters once anyone is ready to give it a go.
You already have a tremendous resource in Dorothy. She and Ron are so supportive of everyone and can tell you everything you ever need to know, including the differences between breed show and ADS rules. Ron has posted some great information on estimating your horse's speed on course while on course.
We don't have any ADS pleasure shows up here -- the closest we get are driving classes in open shows and the carriage driving classes at the Oregon State Fair.
Happs does offer their Trec, which Amy (Clickmini) can tell you about -- you can also read about it on the Happs website...I just know that it sounds like fun.
Another thing you can do at Happs, although it needs to be scheduled so as not to interfere with any events, is to take your horse up and train over the marathon course, including creek crossings, He11 Hi11, seeing deer and cattle, etc. It's well worth the drive and the nominal fee, and would be a fun day in and of itself.
Depending on how much research you enjoy (I live for it), many websites have articles on various aspects of driving, such as Andy Marceaux's articles on Coachman's Delight.
One thing I can't emphasize enough, especially considering Vicky's experience in breed shows: CDE people are unbelievably friendly and helpful -- they don't treat you like the competition but as a friend who is discovering something they love.