India can hold POK, but the method will be playing their game against them (ie pure ruthlesness).
how? The Paki's used the brute Force method in the late 2000s (forgetting the op name)- they even used tanks, Offensive Air and heavy artillery against entire villages. They ended up loosing nearly 700 SSG personel and still couldnt put down the Insurgency.
We dont have the Monetary resources or the Mil Infrastructure to HOLD POK - look at the terrarin. Can we secure the borders of POK - from the north and west? Can we hold a supply chain from India to POK in that terrain. Can we transport Heavy Weapons in an AO where Zero Infra has taken place? The OPFOR for POK logically will be
1. Pak Army
2. Pak based Jihadi Irregulars
3. Haqqani Network
4. Taliban and Afghanistan based Support
5. Chinese Logistics train + Distraction on the China border
At best we will commit 60% of our resources with a Mix of upto date and dated Equipment - To Hold POA you will need at least 1:6 the Man Power simply for Population 'Pascification' keeping in mind the irregular OPFOR. Will we 'Hold' for 12 months? Do we have the abiltity to launch sustain Winter Ops of the kind you are talking. Even 60% is would be execssive for POK. The Paks will logically open multiple fronts across the IB.
Lastly - what is the objective of Holding POK? Obsorbing it into Indian Territory or turning it into No Mans Land or only using as a bargaining chip to negotiate with Pak? How much will that integarion cost - Will the local Population be expelled or integrated? Administration Cost to build up the infra we broke down?
What if We get sanctioned by OPEC and China backed countries? Do we have the fuel reserves for a Holding Op + a potential 2 front flairup - no way china is staying out of this. will the US back us at the risk of Joining a conflict with a Peer Power?