Honestly I'm not so sure. At this point HBO will probably give the show as much resources as it possibly can. They have a mega hit on there hands and while HBO is in it to make money they also care about making quality programming just look at there track record. The wire, the sopranos, etc. How much would a few more scenes with Summer cost 500k maybe? A million? I have no idea maybe more maybe less but I don't think it's like 10 million or something.

Now the show cuts a lot of things but the wolves have been important and they have always had them. They could have easily decided to scrap it in season 1 but they went with it as close to the books as they could. Everyone gets a puppy. So if the show said hey HBO we really need another million for some cgi to make it perfect I think they'd probably get it, or at least some kinda half way point.

I don't think they decided to kill off Summer, I think he's gonna die in the books as well in a somewhat similar way. He's far from the first wolf to die. Plenty have died and GRRM wrote those in, who's to say he didn't tell the show yeah summer dies here. He told them about hodor. Lady died, Grey Wind died, Nymeria is not around. It's not unrealistic for more of them to die. Also names seem to be important and Summer dying means the end of Summer.

I honestly don't think it has much to do with the cgi budget. You know now much cgi the show gets in post production? Check it out in one of the behind the scenes sfx videos they have. Like every scene has some kinda cgi work done to it. They probably use they same 1 or 2 studios to do it. I'm sure they'd probably throw the show a bone if they said hey look we are at max budget but we need a few scenes with Summer can you throw those in for free. Like all the money they have made off the show and will make they could probably work something out.