95 Montero won't turn over when it's cold 10 deg. F but when it's gets warm inside garage turns over fine no issues. Brand new fully charged battery. Connections seem good. No dimming of lights when ignition is turned. So thinking no heavy current draw just click and normal warning lights come one. Has new ignition switch. Going from park to Neutral doesn't help. Any ideas what's going on?

 

Most likely - weak battery. You might have it fully charged, but the capacity is no longer there. This would be worse if you have cold temps. You can try to test the electrolite condition to assess the charge level.
Second possibility is a bad battery connection somewhere (could be ground or positive). Again - wires flex and change in length slightly with temperatures. A small break in the conductor would create a gap when cold. You just have to be patient and go through all components

 

Thank you HunterD looking more at bad connection since battery is brand new. Possible solenoid problem?

 

I would also go to the starter and remove the main feed wire that comes from the battery, and use a wire brush on the wire connector, and also on the nut/threaded bolt where it connects to the starter/solenoid. Could just be corrosion at those connections, or a slightly loose connection. I assume you cleaned all the wire/terminals at the battery when the new battery was installed. Is the starter/solenoid pretty old, or has it been replaced in the past few years?

Good luck with it.
By the way, I own a couple 94 Montero's and while working on the transmission (changing filter/fluid), I noticed that there is no skid pan protecting the tranny, but there are bolt holes for another pan......does your 95 have a skid pan protecting the Tranny oil pan? Here is a pic showing the skid pans coming from the front, and then a smaller one further back which protects the Transfer Case.....and no skid pan in between where the tranny is:

 

Thanks 1960 Stud Hawk, I'll have to check I don't remember one there or transfer case.

 

Yes, it is possibly a solenoid problem.