While the AFRs do participate in search and rescue operations, they generally weren't at the forefront, with the exception of maybe some incidents in the High Peaks. It is usually the full time rangers that deal with search and rescue. I'm sure the state wouldn't have cut the AFR program if they thought they'd not have enough rangers to respond to SAR incidents as a result.
The maximum level of training required to be an AFR in recent years was only Wilderness First Aid (a three day course). I suppose you could say that's another issue concerning state budgets- cutbacks on funding for training for state employees. Some of the AFRs did receive helicopter insertion and evacuation training in addition to their first aid training, but again, they generally didn't make up a main component of the the primary response in emergency situations. If an AFR was ever the first on scene for such a situation, it was usually because they were the closest uniformed member of the department, being that they were already in the backcountry on patrol to begin with.
Its worth noting I think that this decision, as far as we know, does not affect the interior outpost caretakers. The caretakers of the interior outposts at John's Brook, Lake Colden, Marcy Dam, and Raquette River Falls are employees of the Division of Operations, unlike the AFRs, which were employees of the Division of Forest Protection and Fire Management. The caretakers have basically the same responsibilities as the AFRs, except that they are based out of an interior outpost which they staff, whereas the AFRs would go out on roving patrol, spending each night in a different backcountry location. So, assuming that the state still intends to employ the caretakers this season, there will be a regular uniformed presence in the backcountry, at least in the High Peaks Wilderness Area.