Wood was rested for the incredible 43-39 win at the Dragons last weekend but is ready and raring to go ahead of this week's last-eight clash.
Saints had a lengthy list of players missing at Rodney Parade last Saturday but still managed to get the job done.
And when asked whether who if any of the injured and rested players will be ready to return to action against Ulster, Dowson smiled and said: "I can tell you that Tom Wood was tearing up training today and he was making me laugh because he was probably the most enthusiastic player out there and also the oldest."
Dan Biggar has missed both Saints matches since returning from Wales duty due to an abdomen issue.
Dowson said: "He's been training for the past couple of weeks but we don't want to put anyone in who is not quite ready.
"He's certainly been in the group but he's taking it quite slowly because we don't want to rush anyone in case we lose them for a longer period of time."
David Ribbans was on media duty this week and he has completed concussion protocols so will be available against Ulster.
And the likes of Wood, Paul Hill, Tom James, Piers Francis and Tommy Freeman should all be available after being rested.
"It's a constant battle for (head physio) Matt Lee, whose team do an unbelievable job," Dowson said.
"People are coming back all the time and there's lots of grey area about who is ready to come back because it is such a physical game.
"We've got guys coming back, for sure, but at what point I can't tell you as it's often a late decision."