My school has the part time route, too. It's not what most students expect, though. During that part time year, you are NOT taking anesthesia classes or going to clinicals part time. Essentially, the part time track allows you to complete the core coursework required for the MSN, with perhaps a couple of other non-anesthesia/clinical classes, the first year of the three year program. Then, the second and third years follow the same schedule as that of the students in the full time program, minus those courses already completed.
People choose the part time path for myriad reasons - moving to the site of the program, finances (you can get 10 semesters of graduate-level financial aid rather than seven; you can work that first year), tying up loose ends in life before the full time component begins, etc. But, that first year won't do much to considerably lighten your load in years two and three. You will still be absolutely swamped and working your tail off.
Working that first year is easy. Your commitments to school are minimal. Beyond that first year, though, it is exceedingly difficult to work, manage your schoolwork, and maintain your sanity. A few people can manage it, but it often comes at the expense of their family, their health, and their extracurricular activities. Literally, their entire lives become work-school-sleep-eat.
Most people choose to get school over and done with in seven semesters. Most people who extend it to ten do so for a number of valid reasons, but not because they think it will make the last seven semesters any easier.
Hope this helps! Good luck...