"The bread is cold."
춥다 is only for weather or how you feel. You should use 차다 or 차갑다 for describing the temperature of an object. That is my understanding. Similarly, there are separate words for 'hot' for weather and things - 덥다 and 뜨겁다. I would note that the tool tips the website shows for a word doesn't take into account the context, so it shows both even though only one form is acceptable in a particular sentence.
Because 춥다 (추워요) refers to the temperature of air and/or your surroundings; mostly used for the weather. It can't be used for saying that some object is cold.
차갑다 can be used for weather, but it's primarily used for when an object/thing is cold. Especially for saying a thing feels cold when you touch it.
춥습니다 is only used when you're describing how you feel or the weather
차갑습니다 is used when you're describing the temperature of an object
This is how I personally differentiate them:
춥습니다 = cold
차갑습니다 = cold to the touch
So in this sentence, we used 차갑습니다 cause the bread is cold to the touch.. If we used 춥습니다 instead it would mean "The bread is cold" as in like "the bread's feeling cold", it wouldn't make sense lol