The two sides meet at the Emirates Stadium on Saturday afternoon.
This time around the two sides clash with both of them enjoying fine league campaigns, as the Gunners currently sit second in the Premier League table and the Tigers sit top of the Championship.
And as a result of that, Dawson insists his side travel to what should be a daunting fixture for them without any fear or pressure on their shoulders.
“Anyone who watches Arsenal knows they’re a top team and we’ll go there with no fear or pressure on us and enjoy the occasion,” he told hullcitytigers.com.
“We know the story with us and Arsenal in the FA Cup and we’ll go there as a team wanting to win and progress through to the next round.
“It was the same against Brighton and Bury – it’s all about trying to get into the next round of the competition.”
It will certainly be interesting to see how Arsenal manager Arsene Wenger approaches the FA Cup given where his side sit in the league.
This season looks like being their best hope of securing the title in a number of years, and that must surely take precedence over winning the FA Cup.
However, his side have enjoyed themselves in the competition in recent years, having won it twice on the bounce, and would likely be keen to win it for a third time and add that to their history as well.