Company dress code policy mandates outdoor workers to wear pants and no shorts. It is extremely hot with high heat index. Should OSHA get involved?

No. The company is required to assess all hazards and require appropriate clothing to prevent likely injuries. They are not required to let you wear the most comfortable clothing. Outdoor hazards of shorts include cuts and scratches from brush, debris, and equipment, snake and insect bites and stings, etc. All must be considered.

The company assessment ought to be available to you.