The first thing Jon tried to do when the Wall was out of sight was apparition, the most basic and the least magically demanding form of teleportation he knew. If he could do it, sneaking in and out of Winterfell would be child's play. And the further one tried to apparate, the bigger the requirement for magic power. On top of that, doing it wandlessly took quite a lot of magic, but after about ten days of training since his resurrection, he had increased his magic capability by a significant amount. Staying near the Wall greatly helped, as the air near the icy structure was saturated with magic, and he used it to recharge his reserves faster.