Zinedine Zidane's side were held up on the runway in Madrid for four hours the day before the game due to the snowstorm that pummelled Spain and things did not get any easier for them when they kicked off on the snowy pitch at the El Sadar Stadium.
The first half lacked chances with Madrid failing to register a single shot on target.
Karim Benzema thought he had broken the deadlock on two occasions after the break but his goals were ruled out for offside.
"We created very few chances, a team of our quality needs to create more, even when the pitch is difficult to play on like it was today," Madrid midfielder Toni Kross said after the match.
"We knew that our opponents were going to defend like they did. The pitch is no excuse, both sides had to play on this pitch.
"We can't be happy with the result because we're fighting to be top of the league and this draw doesn't help us."
A team of 50 workers laboured throughout the day to make the pitch playable and clear it of the snow that covered the city of Pamplona and continued to fall during the match.
But the conditions inevitably favoured Osasuna, who were happy to sit back and defend deep to afford their visitors as little space as possible.