Greenwood was born in Scarborough, Toronto and from an early age wanted to be a performer; by the time she was in high school at Agincourt Collegiate Institute, she was usually the star of the school plays and concerts. When it came time to graduate in 1980, she feared that she would never get to act again, until a concerned friend gave her a brochure for the American Academy of Dramatic Arts, where Greenwood spent the next two years studying acting.

In 1987, when she returned to Canada, in Toronto she managed to find work for a small night club act called A Wedge of Night, which led to her five-year stint with the Toronto branch of the famous Second City comedy troupe; where she served as both a Writer and a performer - two of her shows won Dora Mavor Moore awards in 1988, and 1992. Shortly afterwards, she and her friends Jonathan Wilson and Ed Sahely developed what she called their "Second City" spin-off, Not to Be Repeated, in which the three would improvise an entire situation comedy in front of a live audience, based solely on ideas and suggestions that are thrown at them from the audience. Other notable appearances in Canada include the popular Sketch shows This Hour Has 22 Minutes and Royal Canadian Air Farce.

In 1996, Kathy found regular work on Canadian television on the family drama series Wind at My Back, where she spent five years, full-time, playing Grace Bailey, a junior radio M.C. in the small town of New Bedford in Ontario during the Great Depression; Kathy's portrayal of Grace Bailey was nominated for a Gemini Award for Best Performance By an Actress in a Continuing Leading Role. In 1999, Kathy was cast as Denise Stanton in the TV movie Switching Goals, starring Mary-Kate and Ashley Olsen. Later that same year, Greenwood crossed the border and commuted to Los Angeles to appear on such shows as The Drew Carey Show, the update version of Hollywood Squares, and the American version of the improvization game show Whose Line Is It Anyway?.