This might interest those willing to know why New York city native speakers of English say their t's.
As refers to pronunciation of \t\, substandard speakers of English in the New York City area seemingly have adopted the glottal stop as the precise phonetic form of the consonant answering to t or tt between a preceding stressed vowel and a following /el/, as in title, battle. A higher percentage of cultured speakers of Scottish, however, use the glottal stop in the same environment, and before an unstressed vowel as in water, bitter, than a higher percentage of speakers in New York City do.
In words like winter, plenty, gentlemen, in which what corresponds to the nt of the spelling comes preceded by a stressed vowel and followed by an unstressed vowel or /el/, American speech either feebly articulates the /t/ or not at all, pairs like winter: winner seeming as difficult or impossible to distinguish without the help of context. Certainly the usual American pronunciation strongly contrasts with the usual southern British pronunciation which possesses a strongly articulated, aspirated, distinctly heard /t/. One would probably regard that sound as the first sound of the syllable to which the unstressed vowel or /el/ belongs, any /t/ that may occur in the American pronunciation probably going not unnoticed or at least belonging to the syllable that contains the \n\. Highly advanced ESL speakers might not notice the difference between the two pronunciations as /‘win(t)•e(r), ‘win•te(r)/. The absence or weakness of the /t/ in such words implies that the pronunciation became too widespread in all levels of American speech so much so one cannot ignore it. Nevertheless, one will notice the /t/-less pronunciation in the vocabulary only in an occasional word for which multiple variants may appear or from which the absence seems especially conspicuous, as at gentleman, the emphasis on the plural of this word in the formula “Ladies and Gentlemen” at the beginning of an address making the absence quite noticeable.
With chiefly native speakers of substandard English in the New York City area a pronunciation somewhat like the British often occurs, except that NYC speakers would rather put the tongue further forward, the tip frequently pressing against the lower front teeth.
[This text 10% adapted by me. Original contents and context belong to Third New International Dictionary, Unabridged (c) 1993 Merriam-Webster's]
As far as AME, sometimes you won't tell winter from winner, mainly if quickly pronounced.