I have the 2520 with FEL and no chains and no loaded tires, so my experience is straight outta the factory. The 2520 weighs more than the 2305, but I don't think too much more as the 2520 is 1,800# before adding the weight of the FEL.
I cleared my driveway (130ft long straight plus another 300ft added on later for horseshoe/circular) last winter when we had 2" freezing slush + 5" wet snow + 3" powder drifting like crazy.
When you are pushing snow, you typically will have the loader in float position and after ten feet of heavy stuff, the tractor will ride up on the FEL, lifting the front tires off the ground. When this happens I back up until the front wheels are "close" to the ground, take the FEL out of float and push with the rear wheels only. The front wheels are just off the ground or barely touching. This lets me go another 15ft or so.
When the snow is wet, you will have to take it slow, but I haven't found this to be a problem since you have to go left and right down the drive way to push the snow off to the sides. You can also scoop and down off to the sides as well. I can't push heavy snow all the way down the driveway and across the road because there is another driveway over there, but you may want to push it across the road and into the ditch in your situation.
The tractor/FEL gets the snow, ice and crap left by the snowplow without any problems for me, all without chains and loaded tires. But again, I'm not trying to be a straight-line plow for 100ft at a time.
I'd try it for a year and see how it goes before investing any more. If I wanted to spend more money, I'd look for a plow or blower before I would bother with the hassle of chains.
I typically clear my driveway with a 42" blower on my JD 335 garden tractor, and I use the chains on that...and what a pain those are. I used to help my dad put the chains on a IH 656 and that was absolutely awful. The 2305 and 2520 are inbetween as far as tire size, so that means they are somewhere between painful and absolutely awful to put on/take off. For that effort, I'd rather take a little longer clearing the driveway with slanting/scooping the FEL. Plus, that's play time!