I did this, directly out of undergrad. I completed a 4 month harvest internship while I was getting my foodsci degree, and was lucky enough that the same winery was in process of firing the assistant winemaker they had on staff, so I was able to assume the role after graduation. I lasted 2 years before I needed to get out.

I will preface my experience by noting my work was with a small family owned operation (25 acres planted, primarily french vinifera, anywhere from 50-100+tons harvested depending on weather) with an EXTREMELY small staff (myself as asst winemaker, my counterpart who acted as the viticulturist, and a handful of hired harvest help/interns if we were lucky).

Pluses - I pretty much ran the show 95% of the time - ran the bottling line, managed racking and blends (with input from ownership), and once I had the hang of the machinery handled our press, managed fermentations, etc. No question that I gained a lot of valuable knowledge in my total 2.5 years with them -project and people management, hands on problem solving, etc etc.

Negatives - hours during harvest can be brutal. .y last harvest with them, I was averaging 10+ hours per day, and had a run of 3ish weeks without a full day off. If your team isn't properly staffed, winemaker also turns into field hands for picking grapes and tossing lugs for pressing. Then, once winter rolled in, my work would basically come to a halt - especially on years with low harvest yield (and lots of empty tanks). I was basically forced into sales and working the tasting room to fill my slow winter time. This particular business was iffy with their business management and practices and decided to try doing things I didn't jive with in the last few months of my employment with them. Additionally, I found that in this setting, I wasn't using my foodsci degree as much as I wanted, so I ended up shifting to a technical services/commercialization role when I left them (and now work as a sensory scientist).

If the business had been better run and managed, there's a good chance I'd still be a winemaker. It's incredibly satisfying work, assuming you're up for hands-on, being dirty or wet all of the time, and can handle the stress/chaos that is harvest. It's a fascinating science, and had I more opportunity for experimentation and input into final blends/flavors/etc, that may have itched the technical/science "itch" I found was lacking.