If you want to save money buy a banged up econobox. Function matters. Looks don't. That's the best economy transportation you don't have to tie or pedal.
Motorcycle economy requires something small and cheap to keep. TW200. Fat tires last 2-3 times as long as other bikes same size, but cost a few dollars more. OEM oil filter and air filter can be cleaned and reused, so no short term recurring costs other than a bit of turpentine for cleaning and oil. Ringed chain and $4 Walmart chain lube lasts 25,000 miles. Couple of O-rings from an industrial supply for the rocker covers, 50 cents each. Even with a TW200, you can spend $40 on filters, chain lube, o-rings, etc., every 3000 miles or so, or do the same with $10 spent more wisely, or $120 at a stealership.
If you have good gear, sleet and hail up to golf ball size don't hurt. Rain won't get you wet. Cold isn't, at least on a 10 mile ride. Remember the tornado that ripped the glass out of downtown Fort Worth 10 or 12 years ago? I rode clear across Fort Worth to order a special tool from the Yamaha dealer that day. The sales people in the showroom backed away as I walked by. The looks of fear on those badapples squids' faces? PRICELESS!! Remember a couple years later when 80+mph straight line winds ripped off roofs and flattened a few houses under construction south of Alliance? I rode through that, too. The police officer who stopped me to tell me it was too windy to ride safely? Oh, you would have LYFAO if you saw what I saw: A low flying porta-potti into the driver door window. Fortunately, the porta-potti was too big to fit through the window and harm the officer, but it did break the glass and the contents, being liquid, ..., well, I felt sorry for the LEO because uniforms and uniform maintenance are expensive, so I didn't LOL, just rode on with the TW lenaing about 30* from vertical into the wind, a big grin, humming a happy tune.
As for cold, good quality rain gear head to toe blocks the wind, 100% polyester longhandles, inner socks, and glove liners, sweats, waterproof insulated boots with composite (not steel) safety toes, and 50/50 wool/polyester hunting socks and glove liners all come from Walmart hunting department, except boots, which come from the shoe department. Treat yourself to a nice set of real insulated, abrasion resistant winter motorcycle gloves. There is no real substitute for warmth AND abrasion resistance. Get yourself some cheap mesh gear, which acts as insulation, but allows air to flow around inside the rain gear to temper overly warm and bitterly cold spots. Even the cheapest functional gear as described will set you back a few hundred, which will by a few hundred gallons of gas for your econobox to go 10,000 miles, so the econobox is a lot cheaper than anything more expensive than a TW200. Used. Home serviced 100%.
Just a couple of my experiences the last time I was without a running cage, for two years, and being in my 50s indicates it wasn't that big a deal in North Texas. So, it is possible to ride when there is a tornado, during hurricane strength winds, any type of precipitation, and cold. It takes nothing more than the right bike and the right skills. People all over the world ride this stuff every day.
Fact is, for most folks (the sane ones), motorcycles are little more than toys, and discomfort is a choice to be avoided. Generally, toys are fancier, newer, have more farkles, faster, heavier, have bigger payments, cost more to maintain, etc., than basic transportation. Toys suck as basic transportation. My son builds custom vehicles, but his and his wife's vehicles are stock except a few carefully chosen options to enhance towing safety. BUT, she has a custom painted golf cart and their 5-year old has a custom painted pedal car, a dropped wagon for rides around the 'hood, and an awesome Yamaha bicycle. The only way to make a motorcycle work for transportation is to buy and build specifically for that purpose. Sure, such a bike will be able to do most anything, it just won't do anything extremely well. Save the extremes for your toy.
A 10 mile ride each way all you need is a TW200 with a properly jetted carb, o-ring chain, and back pack. Even on expressways, if you know how to draft. I've seen 84mph on mine more than once, with stock final drive ratio, give or take a tenth. When the tires wear, go with a cheap JDM street pattern from Chen Shin or similar--they ride smoother and last longer. Any more bike than that is a toy, not transportation. What you really need is one of each!
Some scooters are excellent transportation, too. Just check on the maintenance costs. I know a college prof who rides year around, across town (about 7 miles each way) on a 50cc Chinese scooter. He keeps 2 running and alternates them. Buys them used for zilch from students who don't know how to keep them running. He has a few spares for parts and future riding duties. No biggy when something major crashes, pretty rare so he salvages the parts and tosses the garbage in the can. Only time he doesn't ride is when there is ice, but schools close and he stays home anyway. That's how he affords an Ultra Classic Electra Glide for weekends.
Keep your ears open, and a little cash on hand. Something will pop up sooner or later if you aren't too picky.