THANKS A LOT

Not sure what your criteria for "full spectrum" might be. HPS is obviously not full spectrum by any stretch of the imagination but you might wish to consider it for at least flowering and fruiting. Early stage growth works best when you have more blue light. Solutions would be a metal halide bulb, possibly a conversion lamp that takes both types of bulb, or supplementary blue light. Metal halides are not really a full spectrum lamp, certainly colour rendition is at the same poor levels as halophosphate fluorescents, although advances such as the ceramic metal halide give a wider distribution of wavelengths and colour renditions better than standard triphosphor fluorescents and nearly as good as specialist high colour rendition fluorescents. Still, most people find that metal halide lamps give very good growth. A change of spectrum to HPS may be necessary to produce good flowering and fruit set with some plants, others will do it at the right time or with a change in day length.

I'm not sure what you mean by a cold frame. A transparent container? Cold frames are transparent to allow natural sunlight for the plants and to create some passive heating. If you have no direct sunlight you have little need for a transparent plant house. Transparent walls let light out when artificial lighting is being used, so an enclosed plant house with artificial light should have reflective or bright white walls to keep the light on the plants. Will this be tall enough to grow a mature tomato? Kind of a mini-greenhouse? Are you planning to mount the lights inside or outside it? Outside will be great for lighting and heating the rest of the room, not so great for the plants. Inside would allow you to get more of the light onto the plants, like all of it, but may create issues with getting clearance above tall plants and possibly overheating. The heating may be an advantage with the types of plants you want to grow. Do you need an enclosed environment to keep humidity or heat up? Consider a simple enclosure of white sheeting surrounding the plants and lights.

The entire cold frame is only 3x6FT an will only be little over 3ft high.

I'm looking for a lamp with blue & red bulbs that has enouph power. I just want to make sure one of these lamps won't mess up growth in the plants since it will only be 2 ft away.

Thanks

You can also put your frame over a base of gravel, and run a heating cable through that. I overwintered plants outdoors for several seasons with that sort of setup.

You can buy the whole thing as a kit.