Current rules text of the card:

"After a Polar event is played, attach that card to Realm of Ice and Death. A Polar event card a player owns can be played from Realm of Ice and Death as if it was in that player's hand by removing 1 success token from Realm of Ice and Death as part of the cost of that event."

http://www.cardgamedb.com/index.php/CoC/CoCCards.html/_/forgotten-lore/at-the-mountains-of-madness/Realm-of-Ice-and-Death-AtMoM

If I had a my polar event card attached to this card which I want to play, can the success token then be removed from opponent's side as a part of the cost, or is the token to be removed from my success track?

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?

In order to pay a cost for something, you have to use something belonging to you. In this case, you'd have to use one of your success tokens, not your opponent's, on Realm of Ice and Death.