The only major new characters introduced in season two was Hershel and Maggie. The rest were pretty useless or died quickly.
In the first season there was Carol's husband, that black chick, Andrea's sister, and that guy who got bit (I forget his name, I wanna say it starts with a J).
And yeah, no one likes T-Dog. They "started" an arc with him in the first episode of season two (the whole "we're not important" bit he said to Dale) but that wrapped up literally the next episode and he was background fodder for the rest of the season. He literally went episodes without a single line and he had like maybe 5 lines in the finale. People are just wanting him to die since he's completely useless. Every other member of the group was really quite interesting, except for T-Dog.