Runaways reply there pretty much covers it.
I do suspect they might find a few existing customers of the T-62 and offer them their stored models. The conflict in Georgia was fought with local assets... if it was planned in advance by Moscow the Georgians would have faced a much better equipped force.
Rear area units will have all sorts of obsolete equipment in service... simply because the generally don't actually need anything that is much better.
Current reforms mean however that a lot of obsolete old stuff will be scrapped to free up storage sites and save a bit of money.
What they actually do with the old vehicles is up to them and they will likely scrap the most worn out stuff, perhaps donate some of the more exotic stuff to museums, and then anything that is worth anything they will either offer to existing users in the hope of both getting rid of the vehicles and perhaps making a bit of money with upgrades, or to sweeten another deal.
For instance a country that already has 1,000 T-62s might want to scrap 500 of them but also upgrade the remaining 500, so they could do a deal where they buy another 500 and then get all 1,000 upgraded to a new level... the Russians get rid of 500 vehicles and get the upgrade contracts.
Another instance might be that a country is thinking about buying some Flankers and operates T-62s so to say thanks for buying the Flankers they can gift them 1,000 T-62s from storage plus a few thousands rounds of ammo, plus spare parts to keep their new and existing tanks operating for some time.
The point is that the Russians will have T-62s in storage, but also spare parts and engines and guns and ammo for those guns in storage, and production facilities to make the parts and the tanks and the guns... it would be nice to get rid of everything and remove the 115mm calibre from their logistics train.
So as I said, some will be scrapped, some will become shooting range targets for all sorts of platforms (attack helos, other tanks, ATGMs, etc etc), some will go to museums perhaps, some even to wealthy private collectors, some will be gifted or sold as they are, and some will be upgraded and sold.
I rather suspect nothing will be kept in service because they seem to be going for an all T-72 based fleet till armata/kurganets/boomerang become available.
For all the mess that the MBT fleet is in, where there is a 100mm rifled gun in T-54/55 vehicles and a 115mm gun in the T-62, and of course the T-64 and T-80 which use one set of parts and equipment and the T-72 and T-90 which use another set of parts and equipment and all the four latter mentioned vehicles use a 125mm smooth bore gun you pretty much have 4 completely different and not compatible tank sets.
By withdrawing the T-54/55 and T-62, and T-64 and old model T-72 vehicles and giving upgrades to the T-72s and to the T-80s to make them more like the T-90 then you end up with one gun calibre, and a range of weapons and sensors that are very similar if not exactly the same.
When armata/kurganets/boomerang start entering service the unification of systems and sensors and electronics and weapons and engines and transmissions etc etc will extend from just MBTS to also include IFVs, APCs, command vehicles, engineer vehicles, air defence vehicles, artillery vehicles etc etc etc.
It is going to be huge...