This picture taken from the front of the horse's mouth shows the two small bones in the upper throat to which the muscles and ligaments of the tongue are attached. Being as small as they are, and not intended for any pulling, it's very easy to sprain or tear these attachments. Therefore, under no circumstances should you let anyone hold onto your horse's tongue while pretending to inspect it's mouth. The horse will pull back, and the handler will hold on, and the horse will needlessly then wind up with a sore or injured tongue. Besides, one can't even begin to do a meaningful inspection of a horses mouth that way.
Most importantly, it doesn't work for the horse. A horse has to grind, into very small particles, nearly a bale of hay per day; and can't do that very well with a sprained or sore tongue.
Apart from the reality that you can't even adequately inspect a horse's mouth using the method of holding onto the tongue, there is one much better reason not to. And that is - there is a better way.
Hook your closed fist onto the lower bar of the open mouth and you have both the mouth held wide open for inspection and the horse restrained at the same time. Simply put; you can view the horse's mouth better, controlling it at the same time, without risking injury to the tongue or even getting the horse excited.
Stand facing the horse and insert your closed fist, right or left hand, depending on which side you want to inspect, into the bar area of the horse's mouth, and hook your fist onto the lower bar. Now you've got the horse restrained with your fist firmly and harmlessly hooked over it's lower jaw, and horse's mouth propped open by your fist at the same time. The horse may react and some at first, but if you relax the horse usually will also. During an unsedated animal's dental evaluation, you generally are best to follow the horse around while it tries to get comfortable and cope with your hand in it's mouth, because it's quite impossible to ask it to stand still. So if the horse insists upon squirming around, you simply follow it around, relaxed, and get your inspection done, with someone else loosely at the other end of an attached lead rope.
Now you simply push the tongue out of the way with your flashlight and insert your other hand inside to feel all around the front of the mouth and back to the central regions of the cheek teeth. This way you can thoroughly check the front half of the horse's mouth. If you want to get brave you can pivot your forearm upsidedown and quickly scoot your hand all the way back to the last cheek tooth to check for a hook.
You can't thoroughly check a horse's mouth without using a speculum. That's a bridle-like piece of equipment that holds the horse's mouth open so that you can safely get your hand all the way to the back of the mouth for a full evaluation. One cannot completely inspect the mouth, getting back to some of the most troublesome spots, without the use of a full mouth speculum. Don't let someone claim to have adequately inspected your horses mouth if they do otherwise.
And make sure anyone you take advice from can show you where they got their training by leading you, on-line, to a reputable school they've attended. That's a very reliable test. There are many unsatisfactory farrier schools out there who will also give their students a brief introduction into horse dentistry and leave them quite convinced that they have adequate knowledge and are then even artificially certified in many instances. Those types of equine dental technicians can leave people with the false sense of having their horse properly serviced. But it's not hard to see them a mile away.
I'm not recommending anyone try the above method of inspecting their horses mouth but simply explaining what it should look like when someone who knows what they are doing shows up.
I'm also not discouraging anyone from trying this if they are willing to feel their way along carefully and be ready to learn as they go. Preparing you for some of the pitfalls and surprises you'll encounter would take more time than we have right now. While I'm sure I can't claim this to be an original method of my own, I did think of and develope this method on my own, so with a little ingenuity, I'm sure most people can get it figured out themselves and even improve upon it. This is a very useful method if one wants to safely check a horse for wolf teeth, front hooks, cheek blistering, foxtails, sharp outer edges(cusps) on upper and lower cheeck teeth, inspect tongue injury from bitting, and, among plenty of other things...aging a horse, which is a valuable science in itself that I'm looking forward to posting on when I get a chance.
Knowing how to check your horses mouth, age a horse, even take care of it's feet in a pinch, is an important part of horsemanship and horse ownership.
I'm happy to help you with any questions.
Good luck and take care of those mouths.
Any questions? Just click on the "comments" below.