This is an interesting question, I have to admit that.
Surely, life on exo moons or just satellites in our own solar system would be very different to life on Earth-Moon systems. Their habitats and ecosystem would obviously defer from those we have here. So, let's count them:
1. In this scenario, I am assuming that a moon won't have an ocean on their surface, and instead they have an ocean underneath the surface, and the surface is frozen. So, first of all, pressure.
Pressure would be pretty high in the ocean there, as I have to assume that just after the layer of ocean we have a hot and molten core which maintains the temperature of the ocean and the previous assumption that the surface is frigid. So, that would be a lot of pressure. But on Earth itself we have underwater aquatic animals that live in high pressure under the ocean, so that would not be a hurdle for life - and if we remember the period when the first cyanobacteria appeared and how hard it was for it to survive, we shouldn't be surprised if the same thing happens there. Yes, of course, they might not get enough amount of light from their parent star as they are under the surface but near the molten core, they might get the heat. So, the energy problem is solved, although barely. Now comes the question of intelligent lifeforms. If we consider the fact that the first multicellular organisms were found in the ocean, it would not be an outrageous claim to claim that it would happen in the same way there.
So now we have to define intelligent lifeforms exactly. To me, intelligent lifeforms are those who can adapt to different conditions, make tools and use their environment to their advantage. I didn't include "does not destroy itself" as I think I will be hypocritical if I do that (
). Now, even if we have intelligent lifeforms beneath the ocean - they will have a really hard time. I am saying this because, they would not have access to an atmosphere which hinders them from learning aerodynamics, and therefore takes away the luxury of building rockets and discovering outer space. Moreover, they would have access to barely any wood if aquatic plants there are similar to those on Earth. And even if they have, they will barely be able to go beyond bronze age, as it would barely be possible for any iron to not rust in those conditions. Now there goes better-than-humans intelligent species in this scenario.
2. Now, to the second one. In this case, I am assuming that the exo moon is already protected of solar radiation, has a dense enough atmosphere and a stable climate and is not face-locked like our moon, as already stated by the OP. Now, I have also got to assume that the exo moon's parent planet is in the Goldilocks zone, so that it has enough heat. So, in this scenario, the moon has an ocean on the surface instead underneath it and also has a stable climate, the latter being already guaranteed in the OP.
Now, in this case, as the moon is not tidally locked, we won't have tidal waves in the ocean and therefore multicellular aquatic animals will have a different system of laying eggs or maybe they won't even lay eggs. Now, we have two scenarios within this scenario:
2.1 In this scenario, we do not have a landmass above the surface and therefore there's no chance of terrestrial life. In this case, evolution would be different compared to ours, as we have ruled out tidal waves and therefore we won't have egg-laying aquatic animals or they will have different systems of laying eggs. Now, this scenario will surely have a bad effect on reptiles and mammals will have an upper hand as I have to assume in this case that it won't take long for mammals to evolve out of reptiles as it is a pretty hostile environment for some reptile egg-laying animals and as we have already ruled out land, there won't be dinosaurs, unless you are talking about aquatic dinosaurs. Now, there might be a rivalry between aquatic dinosaurs and the aquatic mammals. Now, we never know how intelligent lifeforms might appear, but if we go by our way of evolution on Earth, we can have intelligent aquatic mammals (merpeople, anyone?
). For this scenario, I am just calling the intelligent aquatic lifeforms as merpeople, for reasons that I don't need to describe (
). The merpeople might not have access to wood, if aquatic plants grow the same way there as they grew on Earth (but, who knows?), and that would be detrimental to their process of making tools. But sure, they can still make tools out of stones and bones which might still aid them. But, again, they will barely be able to go beyond bronze age as there is water everywhere. And for that reason, although they might have access to an atmosphere, they shall not learn aerodynamics and therefore they shall not build rockets and therefore they will not be able to discover outer space.
2.2 Now, this scenario is basically Earth, without tidal waves. They may or may not have plate activities. In this case, we have a very Earth-like process of evolution but with a twist. As I said in scenario 2.1, egg-laying reptiles would have a hard time and that will again lead to an early evolution of mammals and then, evolution of aquatic animals into terrestrial animals. So, maybe, maybe this is a BIG MAYBE, but maybe, we might have intelligent mammals in the age of dinosaurs. This is, again, questionable, but possible too. Now, this will have drastic outcomes. Maybe those intelligent mammals might be just like humans and survive the big reptiles and make tools and advance even more. Or, the dinosaurs will just drive those intelligent mammals to extinction and unless that exo moon's dinosaurs have the same fate as those of ours, we might have dinosaurs ruling the land and mammals ruling the water. But, if the intelligent species manage to survive, as humans survived, they might advance as far as we did and maybe even more.
So, only in scenario 2.2 can intelligent species advance past the bronze age. All of this is merely sci-fi, and if we discover exo moons with life, it is likely that we will discover scenario 2.2 exo moons earlier than the other scenarios. Sure, all of this is merely guesswork, but again, the fiction of today is the reality of tomorrow.