If it's all snowy then it doesn't take place "just" after the battle, isn't it? that's why it feels too early to return to Ostagar when you reach Lothering, I think.
Hmm in the DLC with Sophia Dryden, are there "companion specific dialogues"? when should I do that quest? there is that Levi guy who is at my camp...to launch the quest...
I also have all these presents to offer (the good ones and the prank ones), including the voodoo doll of Alistair, Morrigan likes it so much
(maybe she likes him in secret in fact) there is also a chastity belt, is it a "prank present" for Zevran? o_o I guess that the "orlesian mask" is the prank present for Loghain.
I think the gear you get is keyed to 'level' it's tier to your level (like around 15-16 you get Silverite instead of grey iron). Stone Prisoner, Wardens Keep and Return to Ostagar can be done at anytime you like during the events of Origins. I always did Stone Prisoner immediately after Lothering to get the golem as soon as possible, and I don't think the helmet changes tier. Since you play on PS, you have to determine if what you get from the DLCs is worth doing early or later in game since you won't have any gear mods and need nice stuff for the end battles.
*Edit* Leliana's song, Golems of Amgarrak, Witch Hunt and Darkspawn Chronicles don't take place during the game events but they do provide you with some nice items you can use in the main game if you achieve certain requirements.
There are some companion specific dialogues, but nothing truly different from any other area of the game. It all depends on what kind of tone you want to set for the playthrough. I know in Return to Ostagar Loghain has some really good dialogue, better than Alistair and Wynne and offers some insights into his behavior and feelings about the battle. I actually contemplated having him in my group for it, but then I got to the Alienage and...well, you know how that ends. I ended up Utubing it. All I can say is, being a fan of his, you will have a treat in store for you if you wait to bring him.
Leliana's Song is a prequel in which the Hero is absent, you play Leliana, Golems of Amgarrak takes place after Awakenings and Witch Hunt is the concluding chapter some time after the events of Origins. So those are played outside the main body of Origins at any time you prefer.