Does the comoving size and the observed angular diameter of CMB hot and cold patches change with time in the future?
Yes, the CMB will look different in the future, but that will be in the far future.
Basically the CMB radiation that reaches us today is the CMB radiation that was sent out at a specific radius from us (where the photons had just enough time to reach us today). If we wait longer, then we will recieve the CMB radiation from a slightly larger distance from us.
If we wait long enough then the CMB sky we see will be completely different from the CMB sky we see today. However, the underlying statistics in comoving space (power spectrum etc.) of the CMB will be the same, we will just see another sample drawn from the same statistical distribution.
So yes, the distribution of the comoving sizes of hot and cold patches will stay the same (this follows from the CMB power spectrum being the same), but the positions of hot and cold clumps on the sky will be different.
Edit: Changed the initial phrasing where I incorrectly stated that the angular sizes stay the same. Comoving sizes of the hot and cold-patches will stay the same, but the angular sizes will decrease as the distance from us to the observed CMB will grow. The CMB angular power spectrum will thus be shifted towards higher values of $l$.