Everybody has heard of a Jager bomb: a combination of Jagermeister and Red Bull. It makes for a wild night most of the time; not to jump on the high horse, but the combination of alcohol and caffeine is just not that good for you.
When it comes to coffee and alcohol, it's not the best choice to make. Alcohol is a depressant, which reduces and lowers arousal levels and excitability, while caffeine is a stimulant, which has an opposite effect on the body. It's like if something was pulling you in two different directions – it wouldn't be productive, and ultimately, wouldn't be safe.
The point is, when you're drinking and starting to feel a little drowsy, coffee is not the answer.
There were studies on mice, showing that coffee did not reduce the inhibiting effects of alcohol. Decision-making did not improve and in fact, it seems that people are not as aware of their intoxication when they drink coffee, when in fact, it enhances the effects of alcohol.
However, I don't completely agree with the idea that coffee makes people drunker. I think there are a lot of other factors contributing to any adverse effects of alcohol besides coffee. It just so happens that coffee doesn't help.
Anyway, when you drink your alcohol, drink your alcohol. And when you drink your cold brew, drink your cold brew!