First: check with the US Forest Service Ranger District for the area you want to extract the seedling from. They will be able to advise you on requirements for permits.

Second: While It is feasible to transplant seedlings, you'll need to carefully consider timing, seedling size, and native soil characteristics.

Timing: Ideally you would extract the seedling when it is dormant (generally mid-winter), but that can be difficult in eastern Oregon if the soil is frozen. Early spring would be your better alternative. Our weather is currently too hot and dry for transplanting native seedlings - so wait until early next spring.

Size and Soil: You want to extract the seedling with its root system as intact as possible, particularly the fine roots. This is more easily done with a small seedling growing in loose or sandy soil. I would not attempt to transplant a seedling taller than 2'. If you have the ability, remove the seedling with its surrounding soil and put it on a large (I suggest 2 gallon or larger) pot. (You can transplant bare root seedlings, but that's a more challenging prospect.)

Treatment: Keep the root system moist while transporting. Plant promptly and water well, but don't over-water. Ponderosa pine is intolerant to shade - so find an appropriate planting location.

Water: Use infrequent, deep watering to get the tree established. Trees benefit from having deep root systems, but the way we commonly water lawns (frequently for short periods of time) encourages surface root systems which are more susceptible to drought damage and windthrow. Use a soaker hose around the seedling at the extent of its branch reach. Water slowly (so it doesn't pool on the surface) for 4 to 6 hours. Then don't repeat until the soil 8" below the surface has dried to the point it no longer sticks together when pinched. The frequency of watering will depend on the soil type - but I find that it generally ranges from 2 to 4 weeks between deep waterings. Stop watering by early September so the tree has time to enter normal fall dormancy - otherwise it may be susceptible to winter frost damage. Supplemental watering for the first two years following transplantation will enhance its ability to survive.

Note: My advice is given with the assumption this is a yard tree. If you are attempting to reforest I encourage use of natural regeneration (by naturally occurring seed from local seed trees, rather than transplanting natural seedlings) as the first option, and planting of properly sourced forest tree nursery stock if natural regeneration is unsuccessful.