I've been in the college/university admissions business for over 20 years at several different schools. Where you went do school can matter.
Faculty and admissions professions do consider where the earlier degree is from. This does not mean that private schools are best --- there is truly excellent nursing education at the flagship state schools (Ohio State, Washington, UCLA, North Carolina, Penn State, Florida, Maryland, Colorado, Missouri, Michigan, etc).
Graduate admissions committees also consider where you obtained your nursing experience. Experience from a nationally-known Magnet medical center (Mayo, Cedars Sinai, Duke, NYU, Mass General, etc) will also make you stand out.
If an admissions committee had two applicants with identical 3.3 GPAs and both with 3 years of ICU experience, they would more than likely go with the graduate from UNC over the graduate from South Succotash State.
This does not mean that all is lost for graduates of South Succotash State. A grad of SSS should definitely take advantage of all that his/her school and employer offers, offers, become involved in nursing organizations, seek advanced certifications if applicable, and be engaged at their employer (practice committees, mentoring, precepting, etc).
But if you are interested in seeing how Columbia considers factors in admissions, I think you should contact them directly.