1. However rich you may be, you can't buy it.

Question

2. However rich you are, you can't buy it.

3. However cold it may be, you must not stay indoors all day.

4. However cold it is, you must not stay indoors all day.

--------------------
Which expressions are correct? Are they all grammatical? Then, which expressions are commonly used?

Answer 1

1. How rich you may be, you can't buy it.
4. How cold it is, you must not stay indoors all day

Answer 2

Jahanara is incorrect.

All 4 of your sentences are fine.