I should say they have and don’t have the same definition depending on the context. For example:
1) 今天比前天冷得多了。（It is much colder today than the day before yesterday.) It is a comparison in this sentence.
2) 今年的冬天特别冷。(This winter is ”especially” cold.) We know that winter is cold, this is a fact, but when you say this winter is very cold, it could mean it is much colder this year than the previous year/years.
Hope it makes sense.
冷得多 is used for comparison: 比...冷得多. It means “much colder”.
特别冷 means “very cold”.