Also, winter is the time that birds have the toughest time finding food, so they may find your nice fresh lawn seed pretty tasty. When I plant fresh grass (when it is not too large a space mind you), I sow the seed as per instructions, water well, then cover with clear plastic, just until there is a faint sign of green showing. That way the birds don't get your seed before they get growing.
You need to take the plastic off right away once there is sign of sprouting though, otherwise, you can scorch the grass and kill it. Also, even though it is covered with plastic, the soil can still dry out, so check it often to ensure there is enough water there for it to sprout!
Happy grass growing!