Can I use Dedenne ex's "Tail Swap" attack to move damage counters around if Abomasnow's "Freezing Disaster" Ability is in play?
Yes you can, since "moving" damage counters is not the same as "healing" damage.
Tail SwapFreezing Disaster



×2
Tail SwapMove all damage counters from 1 of your Benched Pokémon to your opponent's Active Pokémon.


Wondrous ShotDiscard an Energy from this Pokémon.
Tera
As long as this Pokémon is on your Bench, prevent all damage done to this Pokémon by attacks (both yours and your opponent’s).
Pokémon ex rule
When your Pokémon ex is Knocked Out, your opponent takes 2 Prize cards.
Can I use Dedenne ex's "Tail Swap" attack to move damage counters around if Abomasnow's "Freezing Disaster" Ability is in play?
Yes you can, since "moving" damage counters is not the same as "healing" damage.