That's okay - I immediately thought "Did I just repeat what she said?" I'm thrilled to have been shown this way of doing it.
"Great minds" you said; after the day I've had, you've made my day to include me in that illustrious group! Have a great day! 
Question for you: is it not best to make herbal teas that way? A lot of time I will dump my Mama's raspberry brew in and make it that way, filtering as I pour out. Am I missing out on something by doing it that way?
I love this method, it's SO much easier & reg iced tea tastes so much better IMO done this way than hot steeped.
In answer to your question: You will get more of the medicinal components if you steep it in boiling water than cold steeping it. You actually get more flavor as well with hot steeping but like I said in my post, black tea is cheap & besides, we don't like bitter tea or the 'edge' (from the tannins) that hot steeped black tea can get.
You can test it for yourself with the herbal tea to see. Use the same amount of water & herb tea. Steep one batch for 5 mins in boiling water, strain & chill. Steep the other overnight in the fridge starting in room temp water. Then taste both. You will notice the difference.
The softer leafy herbs like mint. raspberry leaves, alfalfa, etc give up more flavor & medicinal components to cold or room temp water than the hard herbs like the barks & roots. Barks & root should definitely be steeped in boiling water, some should be simmered & SOME are so hard it's best to cold steep first to soften it & then simmer but that's not really what we're talking about here.
As far as the softer, leafy herbs (like what's used in Mama's RRB) I do mint & alfalfa blend in the fridge & it works fine. It would have more medicinals, vits, etc if I hot steeped it- but it also wouldn't get made as often & if it doesn't get made we can't drink it. My way of looking at it, it all balances out in the end & I don't worry about it. I'm mostly making mint tea for flavor & the alfalfa added is just for some additional vits but it's not my family's major vit source & it's not to heal an illness so it's fine with me. You can up the medicinal components if you do cold steep by either room temp steeping on the counter overnight before chilling it or leaving it in the fridge longer if you cold steep it before using it.
So for maximum vits & medicinal components, make it the traditional way by steeping in boiling water, etc. If it's something like Mama's RRB that you drink regularly & you're busy or whatever & it's cold steep or it won't get made, then cold steep & don't worry about it. If it's something you're making that's just for flavor & cold steeping works then definitely just cold steep & don't worry about it- why make more work for yourself? HTH Blessings ~herbalmom