That chart is DEAD WRONG for Louisiana. Any dog owner who gives HW prevention less than year-round here is going to end up with a positive dog eventually. We're the highest rate of HW disease in the US right now -- nearly every dog I pull out of a shelter is positive. We've had 80 degree days in February and nights don't get much colder, so whoever created this chart is goofy.
The American HW Society's advice is year round for the whole "lower 48" now. They're the ones actually funding research into HW, so if you aren't getting your info from them, you might look into how people who claim to "know" actually know. The post above about break-through infections is quite real: the prevention good but it isn't 100%, so if one slips by, it gets mopped up the next month...unless none is given the next month, and then it grows into an adult.
I would advise you to stop looking at dubious sites, and do a risk/benefit calculation here. It's a lot easier to feel good about decisions when they're based on sound principles, not Internet hysteria.
Step 1: What's the risk of year-round HW prevention? Is it real or even quantifiable? Aside from Trifexis, which a tiny number of dogs don't tolerate and have bad reactions to, most HW meds are extremelywell tolerated. Heartguard/Triheart Plus, Advantage Multi, Sentinel, etc. are given to millions of dogs and have been around a long time. So for a source of identifying the perceived risk here, I would look at veterinary sources/FDA documents regarding side effect incidence instead of the "I'm scared of veterinary medicine blogs" or Dogs-Naturally-type stuff where some authors occasionally radically misunderstand statistics. I like to make data-driven decisions, so I would want data supporting a health benefit for only giving it part of the year. If the primary side effects in FDA files are diarrhea/upset stomach....that sets you up to know what it is you're might be avoiding on the months you aren't giving prevention, if your dog were one of the very few to suffer an adverse effect.
Then compare that to your risk.
Step 2: What's your risk? The risk side of the analysis is pretty clear if you make a mistake in "guessing" which months to give it: your dog could get HW disease, and you can estimate the risk in your area on the American Heartworm Society's website. You may decide that's so unlikely you aren't concerned. (It's also unlikely my dog will get bit by a rabid racoon, but since the risk is death by rabies, I vaccinate...YMMV.) So what exactly happens if your dog is one of the unlucky few in your area that get bitten by a mosquito carrying HW larvae? If you test annually, and it's been at least 6-7 months since the bite, you'll catch it and treat it. OTOH, if the bite was less than 6-7 months ago (say 3 months ago, during your "off prevention" period) and you test, you'll get a false negative, and the worms will grow for another year before they get caught in next year's test -- your prevention this year won't kill them, as they're already too big for prevention (unless you maybe use Advantage Multi, but that's a conversation for another day....most people use Heartgard or its generic equivalent).
Now it's time for treatment. I'll assume you want to use the gold standard, fast kill protocol to treat your dog's HW infection. First you'll need 30 days of an extremely high dose of antibiotics that will trash the gut flora. When that's done, your dog will be injected over 2 months with 3 doses of an arsenic-based compound that's quite painful (causing days of lameness and requiring pain meds in most cases after the injection -- and those NSAID pain meds have their own very real risks). Additionally, your dog will be put on 3-4 months of strict crate risk during treatment (no walk, no off-leash pottying, no playing, no excitement at all -- your dog could die if its heart rate gets elevated during treatment and a clump of dead worms breaks off and clogs a major artery). All this misery will cost you upwards of $1500 in many parts of the US. The treatment has a high rate of side effects, including death (I've seen some statistics that as many as 10% of dogs die during treatment).
So seriously, risk/reward? Avoid some diarrhea vs. risk of heartworm disease? I don't get why it's a tough decision, but maybe it's because I have had to see so many dogs with heartworm disease in rescue. It's an awful illness.