THere is nothing in the rules below about excluded weekends and it looks like your arrival date is not blacked out so you should be fine. I can't tell you how crowded it will be on Saturday, but I can say that it will likely be much less crowded than what you are used to in OH on a weekend. SOmebody more familiar can tell you where to go to avoid traffic.
It's a big claim: Catch a morning flight from almost anywhere and you can be on our slopes the same afternoon. The Park City Quick START (Ski Today and Ride Today) Vacation lets you convert your airline boarding pass into a same-day lift ticket to the Park City resort of your choice. It’s your chance to get a free same-day lift ticket at Park City Mountain Resort, Deer Valley Resort or The Canyons Resort.
You will need to bring the completed, required redemption voucher, along with your same-day boarding pass and out of state photo I.D., to the resort ticket window, to receive your same-day lift ticket. You’ll discover the best skiing and riding you’ve ever experienced, not to mention the most conveniently located resort town in the West. Park City is located just 35 short minutes from Salt Lake City International Airport. Promotional offer valid: Respective resort opening - 12/24/07, 1/2/08 - 2/14/08, and 3/24/08 - respective resort closing 2008.