A Troll in Love?!
Talk to Ug in the Troll Stronghold. He will say he's in love with Aga, but unfortunately she's in a relationship with Arrg. Talk to Aga who seems to be a very romantic Troll and says Arrg has said he will get her Trollweiss Flowers.
Arrg says he won't actually get Aga any flowers and he has many girlfriends and doesn't care very much for Aga. In order for Ug to win Aga's love, he will have to find some Trollweiss to give her.
Talk to Ug about the Trollweiss. He says only someone who spent their whole life in the mountains would know where to find them. Head back to Burthorpe and take a stop at Tenzing's house. Talk to him and he will explain how to get to the Trollweiss Mountain, currently the only growing place of the Trollweiss. He says that you'll need to pass through a dangerous Ice Troll habitat to get to it, and that you'll need a sled for getting to the Trollweiss patch.
Outside the eastern wall of Burthorpe Castle lives the Blacksmith Dunstan. Talk to him and he will make you a sled if you get him the materials he asks for. Talk to him again to get the sled.
He also says you should wax the sled before using it on the mountain. Mix the swamp tar and bucket of wax to get wax. Use it on the sled to polish it.
To Trollweiss Mountain!
Return to Trollheim via Trollheim Teleport or walking. Take the route around the acropolis to the Troll Stronghold, but take the second path north (not the one leading to the God Wars Dungeon). Follow the path north then northwest and you should reach a cave.
Enter the cave (recommended with a Fremennik Round Shield and Protect from Melee on). Go through the cave and try not to think about all the Ice Trolls in there that want to kill you. Leave the cave at the other end and you should come out at the beautiful site of the Trollweiss Mountain, except for the fact that there is an Ice Wolf for just about every tree on the mountain.
Now it's time for the fun part! Equip the sled and make you way south, where you should find a slope heading down to the plateau. Ride down the slope and enjoy yourself!
You should end up at a plateau lined with Trollweiss. Pick one and make your way back to the Troll Stronghold.
Death to Arrg!
Talk to Ug and he will say he's too scared to give Aga the flower since Arrg is still there. Talk to Arrg and the fight will start! You will be teleported to the Troll Arena (Somehow, even though Troll's can't use magic!). He is reasonably easy to kill, although he does hit high so have Protect from Melee on.
After Arrg is dead, make your way back to Ug AGAIN. Tell him you defeated Arrg and Ug will, after a short conversation, finally agree to give the Trollweiss to Arrg.