Basically cold finished steel is free of mill scale and has tighter dimensional tolerances.
If you buy cold reduced sheet it will have been hot rolled initially before being cold rolled to it's finished dimensions. Cold forming versus hot forming will effect mechanical properties too but there's usually a choice anyway- cold drawn tube (welded or seamless) can be supplied 'as drawn', normalized or annealed for example.
Corus have a very informative publication on hot rolled versus cold rolled. It should be available on their web site somewhere. I have a copy, but can't put my hand on it at the mo
From memory:
Basically, unless subsequently heat treated, cold formed products are more prone to cracking when folded, have entrained stresses which can relieve when welding resulting in potentially excessive deformation, and are more prone to cracking under fatigue/flexing. The entrained stresses have also been known to relieve during use, resulting in bowing of the section. Cold rolled RHS has a much larger corner radius than hot rolled - this can be a problem when joining sections as a 'T' because there is a very large gap to fill.
Cold rolled sections are lower cost and are perfectly adequate for certain applications, providing the above is taken into consideration. It's another case of horses for courses.