No, creatures A and B will not stay tapped.
See the first Gatherer ruling on Time of Ice:
The effects of Time of Ice’s first two chapter abilities expire if you lose control of it, even if you immediately regain control of it or cast another Time of Ice.
And the comprehensive rules that back up this ruling:
611.2a A continuous effect generated by the resolution of a spell or ability lasts as long as stated by the spell or ability creating it (such as “until end of turn”). If no duration is stated, it lasts until the end of the game.
So the moment you return Time of Ice to your hand, that ability that was keeping A and B tapped has ended. That ability no longer has any effect on A or B; nothing that happens after that can change that.
Also, when you cast Time of Ice later, it is a completely different Time of Ice that has no connection to the one that you used on A and B.
400.7. An object that moves from one zone to another becomes a new object with no memory of, or relation to, its previous existence. There are nine exceptions to this rule:
(None of the exceptions apply here).
And when it says "for as long as you control Time of Ice", it means specifically that Time of Ice, and not any other objects with that name.
201.4. Text that refers to the object it’s on by name means just that particular object and not any other objects with that name, regardless of any name changes caused by game effects.