"However, it is cold today."
でも is a little stronger. Think of it as で and も。で as in accepting the previous statement as truth, も as in 'also'. So it means "it's like that, but also ...." I find しかし as more hesitant. If i were to say i don't like to cook but i make my own dinner every night i would use しかし。If i were to say i don't like Japanese food but I love ramen I would use でも because the second sentence goes more against what i said in the first.
ですが only means "but / however" when it's preceded by something else; you can't use it on its own. If someone says "it's been hot lately", you could say そうですが、今日は寒いです (sou desu ga, kyou wa samui desu), "that's true but today is cold". Grammatically, a noun or adjective is required before です.