No it doesn't. O2 liquifies at 90K (will just do it in liquid argon). Solidifies at 54K. If you have any solid oxygen component in LN2 then it is as ozone which is a much darker blue and tends to detonate unpleasantly when it thaws. It sometimes happens if you have a wide cold finger dewar open to air and kept topped up for a very long time.
One of the more spectacular and somewhat dangerous pyrotechnicians doing the UK science lecture circuit had/has his own LOX still made out of copper pipe. No reputable supplier will sell him LOX because of the things he does with it. eg Rich tea biscuit + LOX + match. Most chemistry and physics departments have bulk LN2 freely available. Price is similar to beer which makes complex arrays of Peltiers redundant.
The lecturer was John Salthouse and his last touring version was called "Son et Lumiere" an abridged version of some of the more spectacular stunts online at (LOX + biscuit is 13-18s in, LOX+cotton wool 24-34s) :
Music is annoying - original sound track is very loud in parts - actual lecture disturbs dust from the roof and on occasions ceiling panels.
There are other more complete versions on Utube, but technical quality and audience noise is poor. There is also an official BBC version where in the later takes he is sporting a plaster on the forehead after scaling one of the bending an iron bar detonations up a bit too far.
Anyway you will struggle to get things much below dry ice temperatures with any realistic Peltier based cooling. Great for having no moving parts but you have to shift a lot of I^2R heat from the hot side.
Regards, Martin Brown