I have a horse that is body clipped and lives outside, but it doesn't get quite as cold here. She does wear a blanket and neck cover. Your clip will go much easier, use less blades, and look better on a clean horse, but it will take a while for him to dry with long hair, so be prepared. Mine didn't have a super heavy coat and we have radiant heaters in our wash rack and it still took forever. Use tons of Show Sheen, too. Makes the clip easier and look better.
Good luck with your clip. I'm sure you will be fine. I think it was a good choice. You already are worried about how he will look if you don't shave and just getting to the show and riding is enough to worry about.
As long as you have a heavy blanket for night and have an extra in case he rips it or gets it wet. I like to use blankets like I do my own jackets. If I am wearing a heavy jacket my horses wear their heavy blankets. If I am wearing a sweat shirt then the horses wear a day sheet. If tee shirt, horses don't wear blankets.
I never blanket unless I have shaved my horses. And I shave if I am riding a lot in the winter. As you explained when you ride they sweat with the yak hair. Then it's hard to dry and they can get chilled with the cold weather and a sweaty coat.
You shouldn't care what others think, but you should care what YOU think. And showing is fun but it's done to show your best and it sounds like that's just what you intend to do. Good luck and have fun.
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You can wait a few weeks for the temps to rise a bit before bathing your horse. IME a bath is well worth the effort. You can clip faster, and do a lot less damage to your clippers. Also, the lines aren't as bad. Plus he will have grown out any lines in about two or three weeks.
A total bath would probably be out of the question unless it was late spring, early summer. Our hose water is absolutely freezing and we don't have an indoor wash rack, only outdoor. I'd probably just give a sponge bath like someone else suggested and bring hot water from the house and mix with hose water to make it warm. That would be more acceptable, I think, than soaking him with freezing cold hose water and then waiting for him to dry for hours.
When would you all suggest I clip? Someone I talked to said a body clip really only looks great for about 5-6 weeks. But I'd rather do it sooner rather than later and just do touch ups before the show. I don't want him to be a weird, greyish-brown color.
If you are gonna play with the big dogs...clip. The BNT in SS breeds hate "hair"..lol. One tip is to slather your horse with mayonnaise after clipping for a few minutes and then rinse super duper well..it will help tone down the weird coloration.
Everyone has their own opinion, but I think a clip looks best 4-6 weeks post-cliping (except greys). Not that they don't look good past that point; most do. But I think it typically takes that long for the color to look "real".
I have bathed before, several times, with cold water and only 40 degree temps. It sucks, but if you have everything ready to go and do it quickly, and have several coolers to pile on afterwards, it works. I pile on a few coolers then get the horse (and myself) moving - even walk/trot lunging. If you don't want to wait for them to dry get started clipping. Wet clipping is easy and the shorter hair makes them dry extremely quickly.