There don't need to be counters to everything. If there was, gameplay would be one big rock-paper-scissors festival where you either run the counter and can win, or don't and can't. There are things you can do against any type of deck that helps against it, but it won't usually provide a hardcounter except for extreme fringe cases like Freeze Mage vs. Control Warrior. Instead of going this route, Hearthstone has a surprisingly precise microgame (when/how to trade, where to aim your spells etc.) and a less elaborate macrogame (how to plan future turns, when to hold back cards in order to get more value later, etc.) to the point where the game is almost all micro and 90% of decks are curvestone snoozefests where both players simply play the best shit they have on curve and hope they drew better than the opponent. Freeze Mage is one of the only exceptions to this, which makes it such a valuable deck to have in the game.
I don't think decks like this are particularly less interactive than aggro decks where you just push for maximum aggression and face damage every turn. You might interact more with your opponent's minions in such a matchup, but is this really better? The trades are usually obvious to the point where there's no real decisionmaking to be had, and the outcome will depend on whether or not the aggressor drew more aggressive cards than the defender drew answers. Often it's as simple as "do you have a board clear or heal on turn five? If so, you win. If not, I win." Freeze Mage is a deck that's all about planning, utilizing your resources well, and finding a very careful balance between using your burn spells to stay alive and having enough burn to actually win. The opponent has to constantly evaluate whether to play more minions or hold back in order to not lose to board clears, while still pushing enough face damage to pop the mage's block, and constant decisionmaking to preserve every point of health that you can as each little fraction of your life is so important against Freeze Mage.
In nearly every match involving this deck, careful decisionmaking ends up determining whether the mage can Alexstrasza offensively on turn 9 or has to use it to heal himself, whether he can squeeze enough damage in between two blocks, buy an extra turn with freeze effects and win, etc. There's literally no RNG in the deck and every turn is full of difficult decisions. There isn't a whole lot on the board to interact with, but if this is your criterion for whether or not a deck is interesting, it sounds like you don't have an appreciation for the deeper elements of card games. Freeze Mage plays a lot like a M:TG deck, which is something Hearthstone has been lacking in its flood of aggro and tempo decks that mindlessly play on curve and just rely on minions with inflated stats.