> How would you stay warm?
Just like any regular outdoor dog. Find shelter, huddle together, grow winter fur and eventually adapt to the climate. Meanwhile, spend the nights in sleepless shivering fits - but survive. Evolution is brutal, but it works.
> What would you do when it rains?
Get wet! So what?
> What would you eat?
Whatever is available! In any place with a stray dog population, this quickly becomes obvious: Any other animal you can take on (unless it has guns), including other, smaller dogs. Forage for trash or vegetable matter. If humans weren't so crafty and well armed, they'd be yummy too. Stray packs certainly do have a history of nomming the occasional lost human (post-war Croatia for example).
> And most importantly, wouldn’t you be lonely without me?
Hell no. Most of the strays I've seen formed packs or sometimes pairs if they were strong enough to defend their territory.