Canonically, fleets refuel at Gas Giants and via ocean dipping. There's simply not a lot of discussion about scavenging belts and clouds for snowballs.
If fuel were completely ubiquitous, then the general meme of fuel scarcity (Jump requirements, SDBs lurking in gas giants, then entire definition of "High Guard", etc.) would not pervade fleet concepts and fleet tactics in the Traveller.
But it does.
So, all this suggests that harvesting fuel from ice farming random comets and asteroids is impractical and unreliable. If "everyone could do it", then "everyone would be doing it". But, apparently, "nobody does it". Instead they fight for their fuel as a general rule. Securing fuel is important in campaigns. It wouldn't be if it was free to safely take.
Operational strategy is based around the 2 week response time to an attack. When a fleet arrives in a system, the fleet has 2 weeks of impunity before the opposition can react to the presence. Sure, there's always the chance of forces entering a system at any time, but those forces won't be coming as a reaction to the incoming fleet (barring an intelligence failure that predicts their arrival).
As a general rule, fleets rely on strategic surprise. They strike places where the opponent isn't massing their fleet. They bring "enough fleet" to conquer anything expected within the system.
That 2 week response window gives the attacking fleet time to gather, time to refuel, and time to strike.
The dynamics of refueling affect the need or not for tankers. If fuel is free to take, then there's no reason to bring tankers, save to hope empty space. Certainly no reason to bring them with the battle fleet.
If tankers can fuel the fleet faster than living off the land, then theres a tactical advantage to bring tankers with the fleet, top the fleet off, let them proceed deeper in to the system to attack, while the tankers refuel off the land. This lowers the response times of the in system opponents.
If an attacking fleet can jump in to an asteroid field, the fleet can likely mass well before an ad hoc response can maneuver from within the system, and the combat ships can simply delay fueling operations while fighting any defenders off. But even "tanks dry", ships are combat capable as soon as they arrive, as it's typically the jump tanks that are dry.
And, again, of course, if defenders respond, the attackers can forego fueling, bypass the defenders (perhaps trading a quick shot as they fly by) and attack the fixed targets the fleet was likely looking to secure in the first place.
Maybe fueling isn't that big of an issue, becoming routine, with the remote possibility of disaster.