Those "medium-sized" deer are mini-deer. It's one of the transformation spells you can have cast on you, just like the squirrel or bat spells. Someone needs to fall asleep in a mushroom circle to get the spell to cast on you. You might not get it on the first try though, so be patient.

Also, your avatar is a drawing I recognize, posted here. If you do not have permission to use it, I would advise you to remove it. Thank you.

well if you mean to cast on someone else you have to stay in mushrooms till your deer falls asleep about ten minutes

The magic in The Endless Forest often only works if you do it with someone else. ( : Much in the same way as regular antler, mask and pelt spells, you cannot cast a mushroom circle spell on yourself by yourself. Someone else has to cast the spell on you for you.

Thus, you need to find another deer first, and invite them to sleep with your deer in the mushroom circle. When both of you fall asleep inside the circle you both will acquire a spell. Quite often the circles endow a shapeshifting spell for a bat or another animal, so you might need to try a few times before the circle endows the other deer the mini deer spell. Just keep falling asleep in the circle and spell spamming each other till you receive the mini deer spell. It might take some time, but it'll be worth it. ( :

Thanks, but unfortunately I can not log into the game.

Oh, no problem. I downloaded again, consequence: success!!!
So can you do it?