Re-Freeze allows the Ice Monkey to freeze bloons that are already frozen. Giving it extra attack speed allows it to perma-freeze bloons in place, especially useful against Super Ceramics. This is especially so for 0-1-2 Ice Monkeys, which are valuable in the late-game thanks to its very powerful stalling power for an incredibly low cost.
The value of Re-Freeze comes from re-freezing the same bloon more than once. Because of this, a 0-1-2 Ice Monkey is especially powerful thanks to permastalling a bloon by itself aside from frozen-immune bloons, more specifically Zebra Bloons and White Bloons.
0-1-2 Ice Monkeys are excellent choices for stalling Ceramics in place, making it easier for other towers to destroy the Ceramics before they can speed past them. This is because of how much faster the Ice Monkey freezes bloons compared to the freeze durations, thereby almost permastalling the bloons in place. Specifically, Enhanced Freeze freezes every 1.8 seconds while simultaneously increasing freeze time to 2.2 seconds.
One 0-1-2 Ice Monkey is sufficient to solo a Golden Bloon in the earlier rounds.
One 0-1-2 Ice Monkey costs $1110 on Hard Difficulty. On C.H.I.M.P.S., it is a useful tower for stalling down ceramic-heavy rounds such as Rounds 63, along with stalling in the fast Super Ceramics.
Groups of 1-0-2 Ice Monkeys may work at applying Permafrost at all times while perma-freezing the bloons, but it's not as reliable as multiple 0-1-2, as the whole point of Re-Freeze is mostly to perma-freeze and therefore freeze caught bloons for prolonged periods.
0-2-2 Ice Monkeys work just like 0-1-2 Ice Monkeys except freeze one more layer. In practical terms, 0-2-2 isn't very significant, as it only freezes one more layer, and its perma-freeze effect is almost identical unless a tower other than Ice Monkey pops before the Ice Monkey can freeze again.
Do not use this upgrade with Super Brittle, as it will have no effect on it due to Super Brittle automatically gaining access to popping any bloon type including Frozen Bloons.
Crosspathing in BTD6 (Top: Path 1, Bottom: Path 2)
0-1-2 Ice Monkey re-freezing a Golden Bloon after the Golden Bloon attempts to move forwards
In BTD5 Flash, Ice Towers would automatically be able to refreeze bloons. In Mobile versions (except BTDB Mobile since Version 3.6), Ice Towers cannot refreeze bloons. In BTD6, being able to refreeze bloons is an Ice Monkey upgrade.