Hello Agniezska,
Quick reminder: verbs take an -s in the 3rd person (he, she,it): he sings, she walks, it rains. However, some verbs take an -es ending: he goes, it does, she watches.
Now, the correct sentence is:
"He hopes that it will snow tomorrow." As a modal verb, will is always followed by a verb (infinitive form). This is the simple future form.
If you must use "will be", then your sentence will be: "He hopes that it will be snowing tomorrow". This is the future continuous: will + auxiliary be + verb-ing.
Alternatively, you can also say: "he hopes that there will be snow tomorrow". In this case, snow is a noun.
I hope this helps! If you wish to discuss more grammar points in detail, feel free to visit my teaching page and send me a message:
https://www.italki.com/teacher/4812990
Micha.