In some ways, it would be better than Ice Lance. Because it's only triggered on the Attacker's turn (not the Hunter's), it will prevent that minion from acting for two turns. The turn it runs into Freezing Trap and gets frozen (it would, absolutely, need to be coded so that the minion frozen in such a manner neither deals nor receives damage). And the minion would still be frozen on the attacker's next turn. Just like how current freeze effects work. The, obvious, downside is that the Hunter doesn't get to control what is frozen.
I'm not sure what the solution is though. But it's obvious that Freezing Trap is a problem because it's such a massive tempo swing. While it's true that you don't want to Freezing Trap some minions (Defender of Argus, Black Knight, Silencers and so on), there are so many times that adding 2 mana to a minion has, effectively, killed that minion and it's never played again due to how inefficient that card has become. Again, the main problem comes as a result of the rest of a Hunter's Arsenal and the fact that they are constantly putting pressure on their opponent. The opponent cannot sustain the tempo loss from Freezing Trap in addition to being hit by the Clock of Doom and everything else the Hunter is throwing at them.