My convenient bike shop has no gloves. Amazon.com has very little highly rated gloves. Amazon.co.jp doesn't even list ones rated highly in US so I bought wind proof gloves (which weren't that warm in mildly cold condition) from a convenience store and undergloves for 100 yen shop. How can modify gloves to work best?
Gloves are a personal thing and your experience will vary.
I prefer a full-fingered padded cycling glove most of the year. Even when its raining, I'm okay to have wet gloves.
When it is really cold, I prefer a wind-proof outer gauntlet made from leather, that has had beeswax massaged into it. They come up the arm a bit and cover the sleeve's cuff. I'll wear thin merino wool undergloves for warmth. Downside, they're thick and awkward.
On hot days I still prefer full-coverage gloves, to minimise sun exposure. So I have some "ninja lite" gloves with no padding.
On one bike I fitted some motorbike grip heaters under the bartape, but they weren't very effective. Most of the heat was lost to the aluminium bars or the airflow, so I made some "Bar Mitts" or "Poggs" from fleecy lambskin, something like below.
This combination worked really well, the only downside is the 2x 18650 batteries would go flat in about 15 minutes, so I had to run them for a few minutes at a time. Which was workable.
Windproof gloves, perhaps over liners, can work well. Even if you get wet hands, reduced wind chill means they don't get so cold as they would without gloves
You can also wear track mitts (fingerless cycling gloves) over the top of windproof or thin waterproof gloves if you want padding. For almost complete waterproofing you could wear disposable (surgical) gloves under track mitts. You could still wear something warm under the disposable gloves, which would make them easier to reuse as well. This is plan B for me if I'm caught out away from home with insufficient gloves (e.g. lost my warm ones), as I've got disposable ones in my first aid kit.
Another fully waterproof (and windproof) option is PVC-dipped cotton. Because the cuff is cotton, you'd need good overlap with your jacket sleeve to stop water soaking down. The pair I have aren't a good enough fit for on the bike, but if they were, they'd be worth trying, over fleece or knitted warm gloves.
My rides are too long for battery solutions, but you can wear heated motorbike gloves (sadly mainly 12V) or add 5V heater pads to the inside of gloves that otherwise work well. The motorbike gloves would be bulky, so a test would be a good idea - I can ride in big ski gloves without a problem but some people struggle (I'd struggle in the only pair of motorbike gloves I have, but they're very bulky and short in the fingers).
Another possible source: I wear my motorcycle gloves in cold or very wet weather, anti vibration work gloves from the workshop in cold dry weather, and no gloves otherwise (because I hate wearing gloves). Motorcycle gloves are big and bulky, but ubiquitous (at least in the uk), and I already have them. Work gloves with vibration pads are actually a pretty good substitute for proper cycling gloves. As noted above non synthetic motorcycle gloves need a bit of care, but not that much. The worst thing is drying them before riding home if you don't have enough time.
Cold here means down to a few below 0 C occasionally (yes, it does happen even in England). Wet means wet. I ride between fifteen minutes and an hour on paved roads.