He does resist Cold Temperatures but it's in his Infamous 1 Key because the InFamous profiles are caca poopoo currently.
He's able to resist Lucy Kuo's ice which reaches sub-zero temperatures, so he could possibly resist Danny's stuff but that's also dependent on how cold is Danny's Ice Manipulation.
Danny's ice is cold enough to freeze ghosts who can survive and roam space without issue and has frozen pure energy and made it brittle.
Cole is able to resist Sasha's Mind Manipulation via her tar which is above the Ray Field Plague which reduces humans to mindless zombies.
Basically the numbers and layers for Cole go.
Numbers - 10.5 Million given the Ray Field Plague affected the entirety of Empire City.
Layers - Cole's Resistances > Sasha's Tar > Ray Field Plague which turns humans into mindless zombies.
So Danny might be able to posses Cole but he'll either need higher layers or high numbers to do so.
For Danny's numbers and layers.
Numbers - Ember could control the minds of the entire female population of Amity Park which is stated to be a city.
I'm unsure of the city's population number but it would potentially be in the hundreds of thousands at least so in terms of numbers Imfamus is higher.
Layers - Danny's Possession > Danny's Clone Possession > Ember's Normal Mind Control > Sidney Poindexter's Possession > Tucker's Resistance > Syonara Pussycats Mind Control.
Danny has higher scaling in layers of mind control then Coles.
Now onto some questions of my own.
1 - How in-character is it for Danny to use Ghostly Wail?
2 - Doesn't Danny have soul-based intangibility?
3 - How good is Danny's heat resistance?
After these 3 questions have been answered i'll give my opinion on who wins this fight.
1 - It's not in-character for him to use it right from the start. He's only used it in desperate situations against more powerful opponents or large groups of enemies, so he's first needs to see that Cole is vastly stronger than he is before he even thinks about using it and since he wouldn't use it were people could get hurt, he'd need to get Cole to a less populated area or us a light one but that wouldn't pack the force of a full powered one.
2 - Ghosts have more than one intangibility but since Danny mainly fights in a physical state he would use the intangibility he needs to manually activate which is similar to a ghosts default state intangibility which is pretty much soul based. So yes, though Danny doesn't spam this intangibility.
3 - I don't have numbers but ghosts are unharmed by fire, he can withstand energy attacks from other ghosts that can burn and melt objects, and is unharmed by the Reality Gems that burned a boys hand on contact. Lastly, he can survive electricity and Vortex's lighting without being burned. However, Cole's lighting seems to output more heat than what Danny can withstand from what I can see from Cole's profile so he should be able to overcome Danny's heat resistance without much issue.