There are multiple solutions to this issue, most do require a small amount of electricity, and a not small amount of cash. First option is simply a proper coat that is insulated or waterproof - just make sure your choice is practical (there are way too many "cute" dog jackets that are non-functionable) and if the dog is large, often a newborn foal coat/jacket is a cheaper alternative for waterproof warmth. Second option is to supply a heat source of some sort. I do both, my dogs have polar fleece jackets, and they have their heated beds.
My first "go to" for heated beds (or bowls or....) is the K&H line of heated animal products. They have dozens of soft, semi-soft, and hard beds that are specifically designed for dogs (cats and other critters).
My personal preference is their line of hard black plastic pads (the thermo or extreme weather lines) that plug in using anywhere from 25-100 watts. They are not cheap ($30-$200 depending on size and "sale"), but they are incredibly durable. The orphaned wild critters get them in the late spring to early fall, the dogs from late fall to late spring. They are designed for outdoor use, are a sealed, hard plastic unit with a metal coil over the cord to prevent chewing. They come with a faux sheepskin cover, often, but honestly, my critters and dogs prefer to lay directly on the surface, any padding I use they either remove or burrow under, apparently they LIKE the hard surface. They can also be mounted to the side of the dog (or
chicken...) house for the dog to lean against if desired.
I bought five (various sizes) ten years ago - all have been in use 24/7, 365 days a year for over a decade. This year I finally had to replace a few. Upon their annual inspection I noticed one had some deformity to the plastic on the bottom outlining where the wiring obviously was. Although still working, I decided to retire it and avoid a potential melt down situation. The second one was no longer heating, and the third, well my friends neurotic shepherd ate it during a thunderstorm (he ate the crate he was confined in also!).
Second option is the PlayaPet Round Heated Pet Pad. These are great ONLY if you have NO CONCERN about the dog "digging", to make a bed. They are basically a heating pad for pets, encased in a soft vinyl housing that slips into a zippered, soft (but unpadded) cover. It can be used alone or placed in an existing dog bed. Depending on size, they draw 12-20 watts. If electrical consumption is a concern you can opt for the "Pressure Activated" version - it is more costly, but, only draws juice when the animal sits on it.
Both are specifically designed for pets to provide a warming comfort at the vet recommended temperature of 102F (you, personally may not feel the heat, or feel it is "not warm enough", trust me, the critters love the temp). All seem to maintain a constant temp, unlike human heating pads that often cycle up and down. All come with a chew barrier on the cord. I stalk Amazon for them when they are either on sale, or in the warehouse (returns) section. The K&H ones come in multiple versions (identical units) with different names and price points...the
chicken warmer was cheaper than the cat warmer (I got both) and were identical. The baby chick warmer is more expensive than the rabbit/lizard one, and again they appear identical.
Personally, I prefer investing in these heat sources over
light bulbs, heat lamps or using blankets/beds, straw/hay/chip bedding. The former is expensive to use, and the risk of broken glass in the dogs bed, well, not good (and personally I would not like to sleep in a lighted room). The latter because bedding, whether fabric or natural, is nasty, if not useless for insulation once wet, and some dogs like to destroy or eat their bedding. Lastly, frankly, I'm too lazy to check the dog sleeping area daily to ensure there is clean, dry, warm bedding every time the temp goes down or it rains....
PS: the K&H heated, indoor plush cat beds are a winner also with a small vinyl pad that lies beneath the cushion - my small dogs love these (we have at least seven of these beds) as do my friends cats...but again, stalk Amazon for sales or returns (warehouse store) where mine were $30-$50, not the often $120 regular price.