Let's look at where ice types first start showing up in previous games in large amounts:
RBY: Seafoam Islands - between 6th and 7th gyms
Johto: Ice Path - between 6th and seventh gym
Hoenn: Shoal Cave - around 7th gym
Sinnoh: Routes 216 and 217 between 6th and 7th gym
Unova - Winter makes it hard to judge, but Cold Storage (pre 5th gym) always has some, and the rest are always in Twist Mountain (pre 6th and 7th). B2W2 doesn't give the player access until Giant Chasm without Winter, which is post-8th gym.
Kalos: Frost Cavern (between 6th and 7th gym)
Alola: Tapu Village (Between 5th and 6th trials) It's important to note that Mt. Lanakila, despite being the icy area, only has one line more than Tapu Village has access to.
Surprisingly, SM/USUM comes out ahead with Ice type access despite locking the Icy Rock to the Victory Road equivalent. If Galar's icy area to the northeast really is the fourth gym though, that'd be the earliest Ice type of any Pokemon game to date.
So OP, you don't have much to worry about- just take a chill pill.
