Looking on the internet deeply has found these results:

I'm drinking wine is the most popular phrase on the web.

I'm having some wine 154,000 results on the web	I'm drinking wine 1102,000 results on the web More popular!
Some examples and use cases from the internet:	Some examples and use cases from the internet:
The result is a pure, natural product which does not contain additional elements, not even those having wine origin except alcohol, of course, cause it is a liqueur wine. Will you do me the honor of having some wine with me? One minute, you're having wine coolers at homecoming, And the next... You're having wine before lunch. She's downstairs having wine with my dad. And I was sitting there after you left, having some wine. I was feeling so well, I was having some wine of '91. when he called me and told me that the whole family was here. Okay. We were having some wine.	What if I'm supposed to be saving him right now instead of sitting here drinking wine with you? I'm sorry. I'm drinking all your wine. You're still in the running, but I'm not loving that you're drinking wine while watching my brother. I'm not drinking wine that comes out of a box. I'm just drinking my wine. She was drinking wine while we were drinking tea. I'm drinking wine out of a tumbler.

I'm having some wine

154,000 results on the web

I'm drinking wine

1102,000 results on the web

More popular!

The result is a pure, natural product which does not contain additional elements, not even those having wine origin except alcohol, of course, cause it is a liqueur wine.
Will you do me the honor of having some wine with me?
One minute, you're having wine coolers at homecoming, And the next...
You're having wine before lunch.
She's downstairs having wine with my dad.
And I was sitting there after you left, having some wine.
I was feeling so well, I was having some wine of '91. when he called me and told me that the whole family was here.
Okay. We were having some wine.

What if I'm supposed to be saving him right now instead of sitting here drinking wine with you?
I'm sorry. I'm drinking all your wine.
You're still in the running, but I'm not loving that you're drinking wine while watching my brother.
I'm not drinking wine
that comes out of a box.
I'm just drinking my wine.
She was drinking wine while we were drinking tea.
I'm drinking wine out of a tumbler.