The expectations , IIRC, are that the ocean bottoms will have some thermal vents to allow favorable conditions for life.
You only have thermal vents with a hot core. None of these are suggested to have hot cores. Tidal "heating" is what seems to be the primary source for liquid water in all cases. If it gets us into the room temperature range, that might work. But long term stability of that temperature is critical. It can't be bouncing around from one century to next, or whenever.
The thermodynamic barriers are easily cleared on the rocky planets through some period of their existence. They all have/had hot cores. The thermal activity required of complex biomolecules and all the mechanisms involved is not going to happen, in slow motion, in really cold water.
Life is by far the most complex organization of matter known to man. The simplest life form today requires an enormous number of enzymatic activities, etc. going on, all at the same time. For this reason, life on earth has a limited temperature range in which to accomplish this. It is pure chemistry, but on a grand scale.
And modern life has had about 4 billion years to evolve to where it is today. One must assume there were more severe constraints on the start-up, since conditions had to meet exacting requirements. Chemical evolution into the first life very likely had much less wiggle room than that granted by evolution.
Extremophiles aside (they evolve later), one has to consider this enormous complexity and the likelihood of it happening in the deep cold (without a heat source as you noted). Certainly it will be found that skeptics in the biochemistry community number more than one.