Correct.
Any time your commercial rig (truck and empty trailer would qualify or bed loaded on truck, for examples) weighs more than 10k, DOT applies.
DOT number has to be on the truck. Trailers aren’t labeled, just tow vehicles. Magnets are popular for removal when not working. Mine are bolted on steel signs with wingnuts, for quick, easy removal, but better durability than magnets.
As long as you’re not leaving the State, for work, no worries. Take your DOT placard off and drive wherever, when you do leave.
You don’t need Federal Authority (MC number), if you’re intrastate. Kansas requires intrastate authority, but I don’t know about Colorado.
I can help walk you through what is required Federally and help you look up the Colorado specific requirements, if you want my help. I’d even give you my number to chat, if you’re interested.