Your 3.95 UW GPA and 32 ACT are in range for Washington’s Honors Program (UW GPA (middle 50%): 3.85-4.00; ACT (middle 50%): 31-34).
You are qualified enough to apply, but you should definitely expand your search 
@UWfromCA what is the acceptance rate of honors? Is it harder than direct admission to a specific major?
@Furoni, they used to include the acceptance rate on the UW Honors Program’s “FAQ” page, but it was not included for 2015.
If I recall correctly, in 2013 and 2014, they received around 2,600 applications, admitted around 800 (or about 30%) and enrolled around 225. However, for 2015, they received 2,955 applications from incoming freshmen and enrolled 225. I am not sure how this increase in applications affected the Honors Program’s acceptance rate or yield or whether they received a similar increase in applications for 2016. I believe they update the “FAQ” page with the current year’s stats in September or October.
As you may know, freshman applications to UW Seattle increased from 31,611 in 2014, to 36,840 in 2015, to 43,334 in 2016. It will be interesting to see whether this resulted in another increase in applications to the Honors Program.
The only majors at UW that have a “freshman direct admission” pathway are business administration, music and other audition based majors and some of the engineering majors. The acceptance rate for each will be different, but my guess is that most are lower than the acceptance rate for interdisciplinary honors (which, again, is probably somewhere around 25 to 30%).
@Furoni, Washington’s Honors Program has updated its “FAQ” page with data for “Incoming Freshmen, 2016”:
Total applications: 3,802 [28.7% increase from 2015]
Admitted to Honors: 942 [24.8% acceptance rate]
Enrolled in UW Honors: 225
High School GPA (middle 50%): 3.85-3.99
SAT (middle 50%): 1960-2210
ACT (middle 50%): 31-34