Without mods, rain on day 3 of year 1 is absolutely guaranteed, but in other years, Spring 3 can be dry. Aside from sunny days which are guaranteed for the various festivals, the other guaranteed weather days are Summer 13 and Summer 26, both of which will always have lightning storms every single year
As for the rest of the season, it's certainly possible to have 27 dry days of spring; unusual, but if you play enough times it will happen, and I've definitely had it myself. I've also had a completely dry Fall, 28 days of no rain whatsoever. I don't see it's really much of a problem though.