I owned my horse for over a year, started taking lessons at another place on one of their horses.. I had to ask for help picking the horses hoof out- it was so caked with mud and I honestly said I am just afraid of hurting the horse. Trainers response: you'd have to be pretty strong to hurt the horse.
But the reality of it is- I am not familiar with this horses hoof structure, and I find shoed horses feet to be a little harder- I think because the mud can really be packed in there.
I would go over the horses hoof structure- look at photo's so you know the basic layout. Once I find the collateral grooves along the frog, picking the hoof isn't as scary, If it is really caked with mud, I kinda use the side of the metal hoof pick to rub off a chunk of mud more on the outer rim of the bottom of the hoof- somtimes a good chunk will come off and reveal where a groove would be, but if not, then once you scrape to hoof, you can gently pry the mud paddy up some, or manuver your hoof pick to help clear it off- which is a lot less scary then digging. Sometimes if you look in the back of the hoof you can see the edges of where the grooves are.
If its not dried mud, you can brush some with the brush end of the hoofpic if it has one.
Now, if you are unsure of how deep in the grooves you can go- you can kinda just go back and forth with the hoof pic to loosen a bit at a time, or use the brush. If its really caked in tho, the only way to really loosen it may be to pick at it. I always aim to work on the outer side away from the frog if I am unsure. You don't have to get it all in one swipe, even if you just go at it a little at a time, you will eventually get it out ( tho some horses may get impatient, and you can always set the hoof down on your terms, give the horse a short break, and go at it again.)
But I know I am at the end because, quite simply, no more dirt comes out. I use the brush, and look to see if I see dirt. In the end, if you aren't sure, don't go deeper. I am sure you'll be able to notice if there are rocks in the hoof and all. Once you get more comfortable and confident, you'll have an easier time.
Also, there is no shame in asking your trainer to see how you did. Even if they go back and take out a lot more mud, you go back, lift the hoof and take a look for yourself. You can kinda measure with the hoof pick to see how deep it is ( provided you use the same hoof pick) to give yourself a reference point. Once you understand the horses hoof layout, it won't be so scary, and you will be able to pick it out better.