Practice at home just having the baby stand around quietly on a lead. You will find yourself waiting on lead outside the ring for quite long periods sometimes and many of the babies get very bored and rambutious. Nothing like a baby dragging its handler around for half an hour before entering the ring to tire out both handler and baby.
I've only been to a few Trakehner inspections and have never seen a braided tail. Everyone braids manes even though it is not technically required. The only ones I haven't seen braided are the young babies that don't have enough mane to braid and perhaps one mare. I would just groom the tail nicely and clean up hairs along the top of the tail if there are short hairs that distract from your mare's hindquarters.
Don't stress yourself so much about exactly what the mare has on. Turn her out as you normally would. They care less about the turnout at inspections than they do hunter shows. You want your mare to be comfortable with her turnout so do what you normally would do, use the same bit, etc. Braid her mane as it flatters her neck. Warmbloods do dressage, hunter, etc. so it's not more correct to turn her as a dressage horse than as a hunter and vice versa.
We do not trim muzzle hairs. We clean up the long hairs under the jaw and trim the long hairs sticking out of the ears. With the mares we might clean up along the edges of the ears but leave all the hair inside the ears to protect them.
You can see how we turned out a mare and foal in October 2007 at http://www.altamontsporthorses.com/ala.html The filly was 3 months old and barely had enough mane to braid and we faked it on her forelock...it was more of a bun. If you click on the pictures you can see larger versions of the photos and see the muzzle hairs, etc. The filly was very fuzzy as foals usually are. We did not clip her and I'm glad I didn't because she never did shed so she might not have had enough coat in the winter. I did leave a halter on her while she was at liberty just in case she got scared and did something silly it would be easier to catch her. You can also see the clips we used on the reins which I mentioned in a previous post.
I presented another mare and foal at the same inspection. You can see how the colt looked. He is braided but the braids are a bit sparse and stick out a tad. We cleaned up the long hairs under the jaw and only the super long hairs sticking out of the ears and that was it. I was able to get him to finish shedding out by giving him a good currying everyday. He is wearing a new foal halter. I buy all mine from Quillin and I think they look good. There are two photos of him from the inspection. He was 6 months old. http://www.altamontsporthorses.com/kryptic.html
So, the foals are not going to look perfect...they can't. Don't stress out.