'Wonderfully' has two jobs, and they are close but not the same. First, it means 'very well' — 'She sings wonderfully', 'The plan worked wonderfully'. Here it tells you how something was done, and it is warm praise. Second, it works like 'very' in front of an adjective, to push it up high: 'wonderfully clear', 'wonderfully cheap', 'wonderfully quiet'. In this second use the speaker is not only measuring the amount, they are saying they are pleased about it. That is the key: 'wonderfully' always carries good feeling. So 'wonderfully cold' sounds like a happy speaker on a hot day, and 'wonderfully expensive' sounds odd unless you are joking. Though actually — the joking use is real and common. British speakers especially will say 'wonderfully unhelpful' or 'wonderfully bad' when they mean the opposite, and the good word next to the bad one is the signal that they are being dry. The word feels a little more written, a little more polite, than 'really well' or 'super'. In casual speech among young people you would more often hear 'so good' or 'amazing'.