Dogs love tents and will be much happier inside with you than outside in the porch. You’re probably going to need a two-man tent though because one-man tents are notoriously small and only smaller dogs will be able to share with you.
Your dog will definitely need some protection from the cold ground and the best solution for this is a piece of foam sleeping mat cut to size. It won’t weigh much at all after it’s been sized down. If you’re taking a foam mat for yourself and tend to curl up when you sleep, then your dog can share the same mat, otherwise they will need a personal one.
If you use an inflatable mattress, it’s better for the dog to have a separate mat, either laid on top of the mattress if sharing with you, or placed elsewhere in the tent.
You can purchase these totally cute doggy sleeping bags but you do need to consider the weight you are carrying when backpacking. Therefore, it’s more practical to cover your dog with some spare clothes or a waterproof jacket for when it gets a bit chilly.
For wet weather, it’s a good idea to have a small dog towel to dry off wet fur and paws before letting your dog inside the tent.