This question is very situational. For example, I have a Durant with Entrainment and a Shedinja with Mimic. Shedinja mimicked Entrainment that Durant did and then and I switched Durant into the wrong Pokemon, Shedinja used Entrainment on my ally Pokemon which is a pure Water type Pokemon (Inteleon). I was about to switch out Arcanine and Arcanine will use Burn Up, but then I switched in the wrong mon. And I noticed that my opponent has Freeze-Dry. So will Freeze-Dry go through my Wonder Guard Inteleon? (I have not tried it yet I promise).
I checked this through a Replay also. (That Inteleon was Wonder Guard, this one)
The theory is, any Super Effective move surpasses Wonder Guard.
I did not test this through a doubles battle, the way you did, because I’m lazy you only wanted to know about Freeze Dry, if I read correctly.
Hope it helped!