[you're hot and you're cold ]

Looking at appearance-wise there isn't much to tell apart a Pyro and Frost, Light Eater on the other hand do have a different in appearance as Frost are fluffy and Pyro's are slender.

The different between Pyro and Frost Nightmares is body temperature
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[ Smoking hot]

A Pyro's body temperature on average is between 212°F and 315°F, the older the Nightmare the hotter there temperature becomes and can reach degrees up to 1,100 °F (usually when angry)
Nightmare that are betas and higher in rank can suppress their temperature and appear more at a normal body temperature (there are usually a few degrees warmer though but not enough to really notice)
Note: there are some abnormalities, Cataclysm would be considered one of the hottest in his rank but is unable to lower his body temperature under 212°F, there are some Pyro's whose temperatures are below average but they are usually weak and kill off.

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Pyro's also possess fire as an element this flame come in different colors depending on the Nightmare itself but is usually a darker tone (dark blue, dark red, dark green, Exe...) Black flames is something only Ancients possess and is the hottest color flame a Nightmare can use.
because of their extreme body temperatures a Pyro Nightmare can tolerate high temperatures, they are not immune to fire but do have a high resistance against most flames depending on the magical content.
Alphas and Ancients can even consume control over a fire bending it to their will, however if the fire is being controlled by someone else this could be more difficult to achieve and would have to use there own flames to consume and dominate the opposing fire before gaining control.

[you're as cold as ice]

A Frost Nightmare body temperature on average ranges between 32°F to -10°F
Older Nightmares can get much colder and can freeze up to −50 °F to -100°F ( when angry)
Much like a Pyro a Frost above betta can suppress the temperature in appear more normal, but still be off by a few degrees.

Note: there are some abnormalities just like with Pyro's were an individuals temperature will be above or below average of a normal Frost Nightmare.

Because of their chilling temperatures a frost nightmare has a high resistance to the cold but they are not immune to it either.

Frost also possess ice magic, it can come in different colors but just like fire Black Ice is the strongest and something only Ancients possess.

(Alphas and ancients)
They can also use others ice just how a Pyro can consume another flames and seize control over it.

[the element of surprise]

Nightmares can possess other elements but it usually rare or higher ranks
( And limited as In only one additional element )

Pyro: ( fire Nightmare)
Electricity
Earth

Frost: ( Ice Nightmare )
Water
Rock

Both:
Wind
Poison
Sound
Metal

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Note: Nightmares can not possess Light or plant/ life elements.

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All Nightmares possess dark/ Shadow Magic, the ability to manipulate and use Darkness

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Alphys and ancients can possess,
Corruptions and
Corruption is by infecting another with their Barb chains as Plague is used with there fog ( this only effects crops and plant life, the nasty Stuff is in there Tormented form)
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There are some abnormalities or special cases, Malice possesses fire, Darkness, electricity, corruption, plague and the bonuses of being the Nightmare king, as Catty is just fire and Darkness like a normal Nightmare

( I think that all feel free to ask questions if you want)

edit: A frost nightmare is weak versus heat as a pyro is weak versus cold

Re: cook bread or boil water.

she would have Fire, darkness and could ether have any one of the others
earth, electricity,Wind, Poison,Sound or Metal.

Fire will always be the strongest for a Pyro.

Malice has electricity but doesn't use it that much not like he does with fire or darkness, he mainly use electricity when he was posing as a Shadow Hunter.

As an Alpha she will still be able to corrupt others using her Barb chains, but this takes energy to do and will have to regain more before she can corrupt again, and she will be weaker after corrupting something, it's why they don't do it that often, if another Alpha can catch an Alpha after they corrupt something they would have the advantage and could kill that Alpha and claim their territory

Re: sounds could be used different ways, with would be done with there wings amplifying sound, a Roar or Screech could shattered eardrums or send the concussion blast, they can use there voice to luer other to sleep ( they are the only ones who can do that) they can change their voice to mimic others.

Poison, the Nightmare has developed a Venom in there bite, claws, and chains. The venom enter the victims bloodstream causing pain, then paralysis this point the Nightmare could eat there victim alive or let the poison finish them off. The older the Nightmare the more potent the poison is, it could even get to the point where the Nightmare saliva will be like acid

Their faces X"D