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I just finished my first batch of dry ice hash and very pleased with the outcome; no matter the strain, I found that the more mature the plant was, the greater the desired effects; the blonde stuff I got from the 160-mesh bag was the cleanest-smoking of the batch, leaving only a fine white ash and having no discernable tast, although the light aroma of flowers is present when I open the tin of trichome powder I have for stash.
When the weed is cured properly so the chlorophyl is gone, then the vegetable matter that comes through the larger screen will add flavor to the hash and this is when the strain would make a difference in the effects department. THC and CBD are in the trichomes; however, there is still much THC & CBD trapped in the vegetable matter in the form of THCA and CBDA, where the A represents Acid. The human body cannot process THCA & CBDA unless it is first heated through a process called Decarboxylation, which by using heat (smoking or in a boiling bag does it), removes a carbon component that blocks the medicinal effects.
My point is that the strain will not make any difference if you are making very pure hash made almost entirely of trichomes; if you make traditional kief using larger mesh sizes, then the strain will affect the taste and level of harshness. The strength of the weed you start with affects the level of medication.
I really like the dry ice method because the weed doesn't have to be cured first - it doesn't even need to be dry because the water content evaporates right away, practically popping the trichomes off of the plant matter. Smoking this fine stuff does not compare to a simple joint, for I can take one bong hit of a BB-sized dose and within seconds my face is numb and I am high for two hours before thinking I could use another hit.
Another thing - smoking the blonde trichomes produces no discernable smell - as far as I can tell - compared to "greener" hash.
The strains I used in this batch were Sannie's Jack, Madonna, Anesthesia and K.O. Kush, with the Anesthesia being the strongest Indica/Sativa hybrid strain. I first mixed all of the bud & trim in a Ninja mixer to make the batch uniform and will keep the green leftovers to make hash oil some day when I graduate to that level of expertise.
I hope this has been informative.