In general, try to turn the Ice Mech's self-freeze drawback into an advantage. Position the mech to block Vek attacks or emerging Vek, so that it both prevents the damage and cracks the freeze.
Kazaaakpleth is a great pilot for the Ice Mech. They can free themself from ice while attacking an enemy, if one happens to come to close.
If you have Mafan or Bethany Jones pilot the Ice Mech their shields will negate the self-freeze effect of its attack, making the mech more straightforward to use.
Freeze something on every turn. Even if there are no obvious targets, freeze one of your buildings to give it an extra layer of protection.
Get the Aegis Mech's shield upgrade as soon as possible. Gaining a shield after every attack gives the mech a huge advantage and allows you to use it to block Vek emergence, deal risk-free knockback damage, and protect buildings from the Janus Cannon's reverse fire.
Be careful with mission objectives that require 7 kills. The ice mech is very effective, but can be counter-productive when trying for kills.
This squad has very limited knockback ability. Investing in a weapon like Boosters adds a lot of flexibility.
Consider using the Mirror Mech's second shot to crack the Ice Mech's self-freeze.
Satellites won't launch if they're frozen.
Freezing the train will protect it and also stop it from crashing by moving into Vek. A frozen train does not fail the mission, even if it never moves from its start position.