Okay, time for some of my naïve bold predictions that might turn out to be true for some of these cards. In alphabetical order:
Under the right circumstances, Count will be one of the strongest cards in Dark Ages. Like with Minion, my prediction depends on having a high concentration of Counts in your deck. However, unlike Minion, Count helps clean out your deck with its "trash your hand" option. 2 Counts can hit $6 to buy more Counts or benefit-on-trash cards (like Cultist); 3 Counts can either hit a Province or hit $6 and trigger junk riddance/benefit-on-trash cards; and 4 Counts can hit both a Province and trigger junk riddance/benefit-on-trash cards. Of course, this depends on having either Villages or ThroneRooms/KingsCourts, so any buys that aren't used for Count or benefit-on-trash should be used for these cards. In late game when your deck is bloated and you can't get your Counts and Villages/ThroneRooms/KingsCourts to collide, Count provides a nice solution: just gain a Duchy! This nice little perk should enable a Count deck to win many games just because it is so ridiculously fast when duchy dancing.
Junk Dealer will be a dead card in the presence of other non-terminal trashers. I mean, in almost all cases, lonely little Upgrade is better than Junk Dealer. Of course, in the lack of other trashers, Junk Dealer will be strong, but only for the same reason that Walled Village is strong in games that lack other Villages.
Poor House will also be a powerful card. In a deck planned around it, Poor House is almost always going to be worth at least $2 or $3, and often $4, like Harvest. But unlike Harvest, Poor House is cheap and easy to get! Expect to see pro-level games that revolve around who can most effectively use Poor House.
Procession is definitely a combo card. I expect Procession's most powerful combo to be with Border Village: play any $5 card twice, then just gain a copy back again along with a free Village.
Storeroom will be a Duke/Duchy enabler, similar in principle to Horse Traders. All that's needed is 1 Silver per 9 cards in your deck: if you draw Storeroom with no Silver, just discard everything and draw 4 cards. As soon as you have your Silver, you can hit $5 by discarding whatever else you drew. Because of the fact that you can discard Copper without any problem, in non-Duke games, Storeroom will also be a powerful curse counter for Big Money (although not a discard-attack counter).
Wandering Minstrel will be the best $4 village in games that lack combos with other $4 villages (like Fortress and Worker's Village). For perspective, Shanty Town seems to go out of its way to make sure that it doesn't collide with your actions, but Wandering Minstrel does just the opposite. Wandering Minstrel also has a powerful synergy with Scrying Pool.