Roose's death was pretty abrupt. You can't say it came out of no where since, let's face it, it's been obvious in both show and books for a long time that Ramsay offing Roose at some point was a highly likely possibility. But it did feel a tad on the rushed side for it to happen so suddenly. I thought Roose would probably die at some point in the middle of this season (Ramsay himself will be taken down at the end of it), and during their conversation I wondered if it might happen this episode... but did not think it could happen right there and then until it happened (or actually just before it when I realised it could be similar to Roose stabbing Robb Stark).
I was also tempted to think "Wow, Roose just let Ramsay get close enough to stab him and there were no guards around, really? Guess we just have to accept it is that simple since the plot required Roose to die"... but thinking about it, there have been multiple scenes of Roose and Ramsay talking alone or essentially alone, no different to this one. If Ramsay had went after Roose in one of those moments it would have just come down to who got the better of who physically. So if Ramsay surprises Roose with a knife at dinner then it's been fairly well established that he could kill him just that simply. As for the witnesses, I assume Ramsay may have worked out an understanding with the new Lord Karstark, and you can see the fact he is just so bold about it helps intimidate the maester into just accepting it. And for the rest of the Bolton men at Winterfell, I think it's been established well enough that Ramsay is scary enough and perhaps even has enough loyalty (having led the Bolton army etc.) that they'll follow him after Roose's death and won't question him too much on it.
Then there's the question of whether Roose shouldn't have seen it coming and been a bit more careful than usual at this particular moment, since his new son had just been born. Perhaps, but actually I think the show established very well why he didn't, in the scene in Season 5 where Roose tells Ramsay about his birth. He said he was going to throw him in the river as a baby, "But then I looked at you and I saw then what I see now. You are my son." Not exactly much of a soft spot - not killing your own son - but I think that is basically the limit of the great pragmatist Roose Bolton's sentimentality, and it was ultimately his weakness because I think that attitude lasted until the end. He wouldn't kill his son when he was an inconvenient bastard baby, he wouldn't kill him when he was a psychopathic teen torturing people in the basement of the Dreadfort, he wouldn't kill him when his reputation was a liability to his own hold on the North, and he wouldn't kill him even when he was a threat to his new family and even himself.
There's a quite interesting part in the books only, where Roose tells Reek/Theon pretty matter-of-factly that he expects Ramsay will probably kill his new future son, and he doesn't really seem to care. He even talks quite unemotionally about the fact he expects to be dead soon too, so maybe he suspects Ramsay might kill him too. That's not in the show, but I think it still holds true to an extent. He obviously wants to instruct Ramsay to be a better heir and ruler, telling him not to be the "mad dog", and he used his position of the one person with authority over Ramsay to put him in his place on occasion (including with the threat of a new trueborn Bolton). He surely would have wanted Ramsay not to kill him (not just since, you know, he'd be dead, but since it would be a poor move strategically for House Bolton), but I think he basically knew his position - he wasn't going to kill Ramsay, so it was basically up to whether Ramsay listened to his advice and learned, or whether Ramsay stopped listening to him and turned on him. That was the one vulnerability he left himself open to, so obviously that's exactly what got him killed.
Apologies for the long post (once again), but with everything else going on in the show it still feels worthwhile to devote a bit of discussion to the exit of a great character (and actor) from the show.