Sam's answer is not 100% accurate, because [t] and [d] are articulated at the same place in the mouth anyway (the only difference is that the vocal chords vibrate during [d]). Technically the sound that you're hearing is not [t] or [d], but [ɾ] (which sounds more like [d]). The rule in General American dialects such as my own is that both /t/ and /d/ become [ɾ] between vowels and in a couple of other places, like next to an /r/ (so, in words like "thirty"). It's not really a matter of laziness, at least for my dialect; every instance of /t/ and /d/ in those circumstances is pronounced [ɾ], even if I'm speaking formally (the only exception is enunciating very clearly, like if I'm repeating something over a staticky phone line).

You're correct about everything except winter. I've never heard anyone pronounce winter as winder. I've heard people say "winner" instead of "winter", though. The /t/ /d/ rule is for easier pronunciation when you don't want to enunciate every single word. It's just lazy/casual pronunciation. Winder is more difficult to say than winter. It's all about the position of the tongue. Sometimes, when you're speaking, it's easier and it's quicker to make the /d/ sound rather than the /t/ sound, depending on where your tongue is. It's not "winder" because your tongue is already on the roof of your mouth for the /n/ sound, so you can more easily make a /t/ sound. You don't need to go out of your way to make the /d/ sound. But with the word "waiting", for example, your tongue is away from the roof of your mouth, and it's faster and easier to quickly make the /d/ sound than to make the /t/ sound.