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.
Source: Paldea Evolved FAQ; TPCi Rules Team (2023-06-08)

Relevant cards

Note: All applicable cards may not be listed below.
SV2_93
SV2_93
SV2_11
SV2_11