I will try to be as precise as I can be. Weather plays an important role on road conditions in Naran. Near kaghan there are 3-4 spots where there is landslide now the machines have made way but due to rain and continuous water from waterfall water accumulates there. Due to accumulation of water the mud turns into thick sludge and thus the tires slip on that. Now the last night there was good rain and on our return only 1 of those 3-4 spots had sludge and that too was only 10% as compared to day 1.
About tires if your tires dont have enough tread left they will skid and spin. I would advise you to check your 2 good condition tires if their tread is good put them in front, because our cars are only front differential. Get all 4 wheels checked for punctures and if found any punctures go for pukka puncture with tire out of the rim. After all 4 wheels have been checked go for wheel balancing and allignment not before getting wheels checked for puncture because wheel balancing stays as long as tire is on the rim once it is removed balancing goes away.
Your brakes are good but if are an experienced driver of driving in hills you dont need brakes there to stop your car but there are necessary to have on board.
I am not advising you to change the tires at this time because only 2 of them will be more than your fuel expense from lahore to naran.
If any more queries are here feel free to ask