Here are the resources you need to monitor Park City weather & snow.
NOAA – Salt Lake City Area Snow Reporting – snow reports for all Wasatch resorts
Utah Avalanche Center – informative even if staying inbounds
Keep in mind, this is mountain weather. The weather can be very location specific. What happened at 7,000′ is not necessarily what happened at 9,000′.
Pro tip: wind speed and wind direction are super important to monitor.