I want to install a 50 amp circuit breaker in the service entrance box and put the 4 wire 220 outlet for my welder right below the service entrance. I will be using a 50 ft extension to reach my welder when I use it. Is there any concerns with this type of installation? It is too difficult to run the heavy cable through the walls and over the ceiling to the location where my welder is located, but I don't use it that often. The service entrance is only about 3 ft off the floor next to the garage door and the entrance to the main house. Are there any potential issues with such an installation?
Panels at your service entrance can be all sorts of things. Meter only, meter and main breaker, meter and several breakers and spaces, etc.
From your comment it sounds like yours is the kind with several breaker spaces.
Sure, throw a 2-pole breaker in there, come out a knockout with either conduit or cable, and go down to a junction box with a 14-50 receptacle. Myself, I would use a steel box and steel conduit nipple to connect them, then use THWN-2 wire (omitting ground since the steel conduit is the ground).
You'll need #6 copper wire for this, either THWN-2 wire in conduit, or 6/3UF cable or other outdoor-rated cable w/ground. Don't use Romex/NM.
You can use #8 if you want to, but then you'll need to make the breaker 40A. That is legal on a 50A socket because of a Code exception. Given the very short wire run, I wouldn't bother scrimping on the cost of wire.
The cable around to your welder needs to be #6 cordage such as SJOOW. If you already bought #8, change the breaker to 40A. You cannot make extension cords out of NM, UF or any other cable meant for use inside walls or burial. It is too brittle and not made to resist physical damage.