As to your questions about saddle pad or bareback pad...
There are probably as many answers to them as there are horses and people!
Here's what I've done with Circe:
I've done a bunch of no saddle, no pad, nekkid sessions -- these are our "eating while grazing" sessions -- she's getting to hang out and wander as she'd like and munch and I"m letting her get used to my weight. We've also done this a few times in the arena without food and I've moved around a bunch on her back, done "around the world, laid across her, etc.
My purpose for this is to get us both comfortable with full body contact -- I don't like the "only touch the horse" from the saddle training that I have inadvertently gotten over the years. I think it makes both horse and person nervous (or at least can) because the vocabulary of physical contact is so narrow -- if something shifts or is unexpected, there is no familiarity with anything but butt in saddle -- for either player!
I've used a bareback pad with her a couple of times, but I'm finding I don't like them -- or at least the one I have -- on her. She is very round (and has great padding along her spine -- this is one of the reasons that I've been comfortable doing this with her, because I'm not sitting right on her spinal column), and she's got a really round barrel. So, on her, with the cheapo pad I have, I actually feel less secure than I do when literally bareback.
I have also used the saddle some, too -- it is one option when we work together but not a given when I'm on her. (This is as much about reminding me to not push her too hard as anything else -- easy for me to fall into old riding habits when I've got those boots in stirrups!) But if we are going to try to do anything with focus, I use the saddle, so if she scoots or skips or does something unexpected, there is no negative impact for either of us (I'm not grabbing at her because she scooted sideways and I lost my balance, for example...).
So, in terms of saddle, I would experiment -- some horses are really comfortable with little or nothing between them and person. Some prefer some padding. Magick will probably tell you! And experiment with what makes you feel the most secure -- if you are really comfortable w/no saddle, that's great. If it makes you a little tense, then I'd go with a saddle until you're both really comfortable with each other. I think the tack here is FAR less important than having soft, fun, relaxed time with each other.
Bottom line, for me it's about what the best equation is for horse and person comfort. I do use a treeless saddle, so I'm feeling pretty close to the same amount of movement in my saddle as I do a bareback pad. And while I love the bareback game, I don't think starting there is better for either person or horse if it makes either one tense -- and it won't screw up your training (either of you!) to start in a saddle and move to a bareback pad or literally bareback sometime later on in your training.
(Also, as an aside, I don't like riding in a halter -- I know some people do -- I've used it a bit on Circe, but I find that it feels like a really clumsy, imprecise tool. I much prefer riding in a bitless bridle if I'm asking for anything. I just don't think halters were designed for the kind of subtle communication that bridles were -- I don't like how imprecise the pressure is on noses, I don't like the thickness of lead ropes, etc. As I said, I know some people are perfectly happy to ride in a halter, but for me it doesn't feel in any way superior or even equal to a good bitless bridle, whatever version works for the horse/person.)
Hope this is helpful!
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