What kind of paint? What kind of varnish?

Can you bring the chair in to a heated space? This might help. On the other hand, if the finishes were incompatible, that's another issue.

I used Latex paint and a oil based stain. Should I maybe seal it with a polyurethane? Thanks for your help. I did bring the chair inside, hopefully it'll cure.

You may get lucky, but you may also have to start over. "Dry to the touch" is not enough when switching between latex and oil finishes. It would've been best not to do this at all, but at the very least you should've let the latex cure completely (like for a day or two) before topcoating.

You have used three terms for the materials you used---latex, oil based stain and varnish. Stains are not finishes and may not dry when applied to a painted surface.

If you painted the chair with latex paint and then applied an oil based stain, the stain cannot be absorbed into the wood---the intended and designed purpose---so it can only sit on top of the paint. Eventually the oil based carrier will dry, but the stain particles wlii still be smearable.

If you used an oil based varnish over the paint, the varnish may be too old and will not dry properly.

Give the chair a couple of days in the warm interior and check it. If it is still wet, simply use paint thinner to get as much of the stuff off. Thinner will not hurt the latex(unless it was not dry) and you can sand lightly and try a new varnish.

In addition to all the misuses and incompatibilities noted above, water borne finishes can take up to three weeks, at a temperature above 65 degrees, with nothing on top, to properly cure.