Use Enchanted Broom. It is fast enough to swap enemy pet before it can cast anything so it can wreck enemy team strategy. But if he has double weather changer, you are screwed anyway (like Little Helper and Tiny Snowman).
Anyway, these teams can be countered quite well by these two group of pets: Rabbit (any fast one with speed higher than 325, like Grassland Cottontail S/S, Rabbit S/S...) and a snail (preferably one with high health, like Shimmershell Snail or Scooter).
These pets take reduced elemental damage from Deep Freeze, Call Blizzard, Frost Shock, Snowball, Ice Lance and Ice Tomb and also will make the stuns from Deep Freeze and Ice Tomb irrelevant.
Drawback is that both snails and rabbits have an attack which is weak against humanoids (Flurry and Acidic Goo), however snails have attacks strong against humanoids (Absorb) and elementals (Dive) and rabbit is there not for nuking but for avoiding damage (it avoids damage in 3 rounds in each 5) and stuns.
Probably another good 3rd pet to pair these 2 critter with is Scourged Whelpling H/H. You can either change the weather with it or put a dot on ground. Another ability would be Plagued Blood, excellent for self healing and Tail Swipe. It is so slow that Tail swipe will always hit twice meaning it will heal you twice through Plagued Blood. Note that Death and Decay + Plagued Blood are both strong against humanoids so Whelpling will most likely be paired against the snowman and that is situation you want to avoid. If snowman is faster, than it goes Deep Freeze + 2x Basic attack IN A ROW without you doing anything so you would eat over 1000 damage.