"It's very cold" is correct because you are describing 'it' which in this case would be the weather. Here, the word 'cold' is an adjective. If you want to be more specific you can say: "The weather is cold." "There's a lot of cold." would not be correct as the word 'cold' in this sentence cannot be used as a noun. A sentence where 'cold' can be used as a noun is shown here: "There's a lot of fun activities you can do in the cold." The 'cold' is now a noun that means a low temperature; a cold environment; cold weather.