"I was concerned where money would come from to do (the house) up. DP insisted all would work out though and so the house was bought"
This was a big, big mistake on your DP's account, and on yours for agreeing. It is really important to separate an economy decision (buying and paying for a house and its maintenance) from an emotional one (we don't know how to pay for it, but hey, I'm sure it will work out). Before buying a house, you both must sit down and make a budget: how much money comes in, how much money the mortgage payments will be, how much for food, car, insurance, house maintenance, etc etc. Money issues don't ever "work themselves out" without the actual money being there. Coins don't grow out of the tree of love.
On other accounts, being on the mortgage and being listed as a house owner are two different things. You should have been written down on the house ownership contract (deeds?) as a joint owner, regardless of the mortgage, as you and your DP had agreed the house would be for you both. If you didn't do it, this is the first thing you must do. Believe me, it will save you from a LOT of heartbreak and future problems.
Your DP is being a bit of an ass making these distinctions about "yours" and "mine". He is supposed to be building a relationship with you. Having a warm house in winter is crucial, much more important than a new laptop in any case. Your DP knew about your money problems before buying the house, and it was him who pushed to get it done.
In my opinion, the first and foremost to do for you two right now, is to sit down and agree, before all, that you are on the same wavelength: that the house is the place for you, as a couple, to build a life together. The house and all its contents has to belong to both of you, otherwise one of you will always fee left out and alienated, and won't fight for the project or feel like a part of it. If you let this fester, it will destroy your relationship.
Once you agree on this, you need to make a budget. And a very strict one. You need a separate account for vital things that the house needs to become inhabitable (heating being one of them). You need a plan and a fix amount for each of you to put on that account monthly, no excuses. And most important of all, you need to start working as a team. Ask yourselves: "what are we willing to achieve together?". Do you want your house to be your love nest, the place you grow old together, or a point of friction and a reason to fight? because the decision is only yours. And if you are not even able t agree in what to do with your own house, there will be little in your life as a couple that you will agree on.
Good luck!