Where can I find spicy peppers?

Things that protect you from environmental effects can be found near the border of the effected areas. For the peppers, they can be found on a stalk growing out of the ground, 3 to a plant. Also keep an eye out for red "summerwing butterflies", you can make a potion out of them to hold off the cold as well.

You can find some peppers near the gate to the cold zone and under the bokoblin platform. Butterflies are near the platform as well.

I just found it. It is near the gate to the colder part/hill just by the citadel of time.

It is just the little plant near the gate: