Yeah, Winona State University does provide scholarships based on merit. Here are some of them:

WSU Foundation Board Scholarships
Total Worth: $4,000 per academic year
Eligibility: $4,000 per academic year
Minimum Criteria: Top 5% or 3.90 cumulative high school GPA on 4.0 scale of graduating class and 28 ACT/1320 SAT
Separate application needed: Yes

Outstanding Academic Honor Awards
Total Worth: $3,500 per academic year
Eligibility: $3,500 per academic year
Minimum Criteria: Top 5% of graduating class or 3.90 cumulative high school GPA on 4.0 scale with 32 ACT/1470 SAT
Separate application needed: No

Presidential Honor Scholarships
Total Worth: $1,000-$2,500 per academic year
Eligibility: $1,000-$2,500 per academic year
Minimum Criteria: 3.20+ cumulative high school GPA,26+ ACT , 1260+ SAT
Separate application needed: No

Winona State University provides aids at an average of 7700 per student meeting 52% of students need. 98% of students with need receive financial aid at an average of 5592 need-based grant. They also provide other scholarships including Alumni Society and Intercollegiate Athletics.