Eowyn, Restless Warrior. Obviously looking for a combo with Freely Across our Lands Here. Quite good. However, I would consider some other form of token reinforcement and go with Eowyn, Lady of Ithilien. She's that much better.
Lady of Ithilien would be good, but also consider
Eowyn, Restless Maiden, who combos lethally with multiple copies of
Dernhelm's Blade to potentially lay on multiple direct wounds. Play one on her, wound a minion, discard it with her text, then play another from hand to wound AGAIN. I love that combo.
Theoden. Okay....you're running 2. I'm not sure why you're doing that, since you can only have one copy of a given comp. For a good solid starting companion, I'd check out Gamling, Defender of the Hornburg. He's nice at grabbing your possessions fast.
Defender of the Hornburg IS a good idea, but I like starting with Theoden. If you DON'T and instead rely on drawing him from your deck, I'd recommend
The Renowned, since you should have Eowyn and Eomer around to make Theoden big.
For extra companions, Hrethel is good, as would be Eomer, Third Marshal of Riddermark. You see, Rohan alone cannot pack a big enough punch with archery by itself, but with some fighting abilities also, it can do decently.
Third Marshal is ALWAYS good, especially with wounding decks, but I like the version you're using. Makes your deck fun and unique. In hindsight, I think I'd start HIM with Eowyn to get the full effects of his text...plus it gives you an 8-strength companion to start with. Not too shabby, that.
I have to get off soon, but a couple more tips, run 4 Riddermark Jevelins, Sword Racks, Eowyn's Sword, Dernhelm's Blade and Eomer's Spear, Trusty Weapon.
I agree with all of that. Here's what I'd recommend:
Frodo, Resolute Hobbit w/
The Great Ring OR
The Ring of Doom OR the best Ring you can manage
Eowyn, Restless Warrior (starting)
Eomer, Skilled Tactician (starting)
Theoden, The RenownedHrethel, Rider of RohanRohirrim RecruitMerchant of WestfoldRiders of the MarkMerry, SwordthainEomer's Spear, Trusty WeaponEowyn's Sword, Dernhelm's BladeHerugrimRohirrim HelmHeavy Chain x2
Rohirrim Mount x2
Swift Steed x2
Riddermark Javelin x4
Rider's Spear x2
Work for the SwordHamstrungKing's BoardSimbelmyneLet Us Be SwiftBlood Has Been SpilledBorder PatrolFreely Across Our LandDoom Drove ThemSword Rack x3
Swordthain and your Sword Racks enable you to pull back plenty of possessions, eliminating the need for
Mustering for Battle and one of your
Freely Across Our Land. I added in
Doom Drove Them to give you another token condition. I also added
Trusty Weapon and
Dernhelm's Blade, since they work very well for direct wounding and nice pumps when you need them. Took out
Rohirrim Bow and added in more
Riddermark Javelin. Moved Eomer to the starting fellowship and changed out your Theodens for
The Renowned. Also changed Frodo to a more useful version (since the threats aren't as big a deal) and a better Ring.
The only real downside I see is a lack of healing. If you can fit them in, a couple copies of
Rohirrim Shield would do you some good, or perhaps
With Strength to Fight.
Thundering Host would double as a nice pump; you could swap it in in place of
Hamstrung and perhaps even
Work for the Sword or one of your many possessions.
Just some thoughts. It's your deck, so do what YOU want with it. If you feel any of us are trying to change it too drastically, then go with YOUR gut, not ours.
I tried to stay faithful to your original deck ideas with my suggestions, but again, if you don't like something I recommended, then by all means, don't do it!
Hope this is helpful, though. Good luck!