Join Date: Dec 2008
Location: Mostly living in the basement
Programs: Free Agent Level 2; MR LT(!)TE, HH SE, ALL SE, BAC Silver, DL MM, UA PS, 2V Fanboi, CBP GE
Posts: 5,347
You can totally walk from T3 to T1. Just go left along the roadway as you leave T3. There are sidewalks the whole way. You do not have to go via the parking lot if you stay next to the terminals. It's not the most pleasant walk, but it's doable and probably takes about the same time as going via AirTrain.
However, if it's raining the AirTrain route is completely covered/indoors.