Would a unit played at reaction speed in response to the trigger at Frozen Fortress also take the dmg?

Yes — if the unit is sitting at that same battlefield when the Frozen Fortress trigger resolves, it takes the 1 damage.

"Deal 1 to each unit here" is a non-targeting mass effect, so it's evaluated at resolution, not locked in when the trigger goes on the chain. FAQ #12286 makes this the flip side of the empty-battlefield case: if it resolves with no units there, the instruction does nothing — which means whatever is there when it resolves gets hit, including a unit that entered in reaction.

One catch: a Reaction unit still only plays to your base or a battlefield you control (Rule 813.3.a). So to actually land "here" you'd need to control the Frozen Fortress battlefield. Play it to your base or a different battlefield and it isn't "here," so it takes nothing.