Freezing Band: Each opponent can't draw more than one card per turn.
In the scenario you've presented, it's P1's turn (since they played Freezing Band). There's no mention that P2 drew a card earlier in the turn. If P2 had not drawn a card earlier in the turn, P2 can exhaust a resource to draw a card (using the effect from
Invocation) one time. They would not be able to use Invocation's effect to exhaust a resource and draw a card again because of Freezing Band.
If P2 had drawn a card prior to Freezing Band coming into play, they would not be able to successfully draw a card by exhausting a resource and using Invocation's effect. Freezing Band only cares about whether a card has already been drawn this turn, not whether a card has been drawn since Freezing Band came into play.
Hope this helps.
Dylan Northrup (aka Doc X)
Level 2 Vs Rules Knowledge, Player Management
Level 1 WoW Rules Knowledge, Tournament Organizer
Level 0 Time Management