Dear Spring Entry:
Your information is quite correct. Most universities in the US admit students in the Fall session. Most universities also accept applications for the January session as well, however the number of students admitted is nominal. There are no particular universities that specialize in January entry. You can find a list of relevant schools here:
iMahal Education Section: List of Business Schools in the US.
If admitted, foreign students can enter the US in the Fall or Winter, provided all legal requirements for student visa are satisfactorily met.
In our view, getting admitted into a good school should be your highest priority, and not whether you can begin your studies in September or January.
Just a matter of terminology. The US colleges and universities generally follow one of the two systems: semester system or quarter system. The academic year, excluding the summer, is either 2 semester or 3 quarters long. Typically a semester is 15 weeks long and a quarter is 10 weeks long. The Fall semester, starting in August or September, is the start of the academic year. The subsequent semester, called the Winter semester, typically begins in January. Under the quarter system, the Fall quarter, beginning in September, is the start of academic year. Winter quarter begins in January and the Spring Quarter typically begins in April.
We wish you continued success.