You can do that. Just set the temp to what you want for the season. It's less than ideal simply due to space.
Not sure what your budget is but you can also look into a swim spa and have it do both. Swin Spa's are not cheap though. Artesian (Tidal Fit) makes a good swim spa. Something like the EP-12 might do exactly what you want in the space you have. The DTL would be ideal for you but it's too big for your space.
The single most important thing to look for is the dealer. Most mainstream manufacturers (Hot Springs, Caldera, Marquis, Artesian, Bullfrog) make a quality tub, it's the end support that matters most to you as eventually all tubs need service. A good dealer is a blessing, a bad dealer is a nightmare. I have an Artesian tub and a great dealer. I looked at a lot of tubs and dealers before deciding to buy from a dealer 100 miles from me as they had the best reviews and my in showroom experience was far better than with the dealers within 25 miles of me. I had one small initial issue which the dealer promptly responded to me, a callback from a tech within 10 minutes who quickly guided me thru resolution of the issue (an air bound pump).