AFAIK, according to the old legends, vampires weren't that vulnerable to the sunlight.
They really WEREN'T vulnerable at all. They could walk among the daylight. Some legends even say, during the day, they would even blend INTO society and be indestinguishable from normal people(they could be your friend, or co-worker, go to work, go to school, and act as a functioning member of society). It was just in the night, their powers and cravings would be at their peak.
I personally, do like the modern depctions only because the night is a powerful thing in horror. Night just looks better whenever you think of vampires. Gothic night, huge full moon in the sky, it just fits. Not just with vampires, werewolves, zombies, demons, even slasher killers. Jason Voorhees is much more scarier when he's chopping people up during the night than in broad daylight. Camp Crystal Lake is much more creepier a place at night. It's kinda a natural thing, because the night, itself, is it's own obstacle. We are creatures of the daylight, functioning mainly during the day. Duriing the night, mostly, we are tired, disoriented, obscured by darkness(we lack natural night vision). For monsters and horror lore, to me, it just fits it like a glove.
But yeah, Dracula can walk during the day. He did in Stoker's novel.