Does someone promote their newsletter through ads?

I've created ads for a different business to increase subscribers, but it was mostly to reduce taxable income. To see if it makes financial sense for you, you'll need to quantify the lifetime value of each new subscriber. That can be hard for a newsletter since the value can change as the size of the audience changes. For example, you might be losing money per customer today, but eventually the value could increase once you hit a certain number of engaged subscribers. A step-change in lifetime subscriber value could occur if you start promoting your own product, gain a sponsor, start selling ads, etc. It truly is a hard thing to quantify.

With all that said, there is something to be said for the intangibles. If more subscribers motivates you more to create a stronger newsletter, that could be worth more to you than what the finances say.

It really depends on one question. Is your business is writing newsletters or you write the newsletter around any other product/service that you do? For the former, I think running ads on social media makes sense, but for the later probably your goal is to nurture your visitors or potential customers - so rather direct traffic to your site and find ways to communicate strongly why they have to subscribe to your newsletter.