Since a dragons breathe weapon isn't actually magical would it be colder than -50 to get by this ring? Or would this ring allow a player to bypass a white dragons I've breathe?

Describe the following to your players to provide better immersion:

This metallic ring is pleasantly warm to touch. On it's red surface you can clearly spot intricate carving of flames.

-50°F is about -45°C

Just says cold damage. Doesn't matter if it's magical or not. 

I like how this is just a ring of resistance (A rare item) for cold damage and some more flavor text that I could see players arguing about whats -50 degrees and what is cold damage. But it is listed as uncommon.

I would think that ice breath the way we imagine it would freeze things similarly to the effect of liquid nitrogen or something, and the interwebs tells me that liquid nitrogen is colder than -100° at least.

Quote from datphatman >>

I would think that ice breath the way we imagine it would freeze things similarly to the effect of liquid nitrogen or something, and the interwebs tells me that liquid nitrogen is colder than -100° at least.

 Liquid nitrogen (LN) is an inert cryogenic fluid with a temperature of − 196 °C [− 320 °F]     ................. burrrrr.... I triple dragon dare you.

That design is so cute!

The ring of baby ermines

I love it

What if you’re playing as a Lizardfolk? Since the player is cold blooded, would this ring help regulate the Lizardfolk’s body temperature or does the ring only protect from damage? 

One of my players is a kobold in the Northlands of Midgard.  He definitely wants the ring to keep warm.

All gases, when cooled, condense. Two gases often used in their liquid forms are nitrogen and helium.

Nitrogen gas, when cooled, condenses at -195.8 Celsius (77.36 Kelvin) Liquid helium boils at -268.93 Centigrade (4.2 Kelvin). Helium does not freeze at atmospheric pressure. Only at pressures above 20 times atmospheric will solid helium form. Liquid helium, because of its low boiling point, is used in many cryogenic systems when temperatures below the boiling point of nitrogen are needed.   Breath Weapon=boils at 5 degrees Kelvin [Tiamat]

Quote from Fistandantilus >>

Quote from datphatman >>

I would think that ice breath the way we imagine it would freeze things similarly to the effect of liquid nitrogen or something, and the interwebs tells me that liquid nitrogen is colder than -100° at least.

 

 Liquid nitrogen (LN) is an inert cryogenic fluid with a temperature of − 196 °C [− 320 °F]     ................. burrrrr.... I triple dragon dare you.

All gases, when cooled, condense. Two gases often used in their liquid forms are nitrogen and helium.

Nitrogen gas, when cooled, condenses at -195.8 Celsius (77.36 Kelvin) Liquid helium boils at -268.93 Centigrade (4.2 Kelvin). Helium does not freeze at atmospheric pressure. Only at pressures above 20 times atmospheric will solid helium form. Liquid helium, because of its low boiling point, is used in many cryogenic systems when temperatures below the boiling point of nitrogen are needed.   A Breath Weapon boils at 5 degrees Kelvin [for Tiamat]

Quote from mtjeant >>

What if you’re playing as a Lizardfolk? Since the player is cold blooded, would this ring help regulate the Lizardfolk’s body temperature or does the ring only protect from damage? 

 "Cold blooded" animal's blood isn't actually cold. It means they just change their body temperature according to the environment. If it's cold outside, their body become cold too. Hence lizards like to sunbathe to stay warm.

"You and everything you wear and carry are unharmed by temperatures as low as −50 degrees Fahrenheit."

Therefore, the answer to your question is: Probably yes. If the outside air temperature drops to below 4°C, most lizards will start to lose their movement ability and eventually possible death. Unable to move due to it's being too cold out there seems like a harm caused by temperatures to me.

For a silver dragonborn with cold damage resistance, in a warm midsummer setting, I think I may have made a big  mistake. 

It is odd that the Ring of Cold Resistance is a worse version of this ring—and way less cute—but is Rare. If this ever comes up in my games, I might swap their rarity, remove the attune requirement from the RoCR, or just replace the RoCR with the RoW.