The active player has a choice: either he gets a
Thing in the Ice with eight ice counters and four +1/+1 counters, or he gets a Thing in the Ice with eight ice counters and two +1/+1 counters, or he gets a
Thing in the Ice with four ice counters and four +1/+1 counters.
As
Thing in the Ice is entering the battlefield, there are two replacement effects that want to be applied:
Master Biomancer's, and
Thing in the Ice's own ice-counter ability. Applying either of those abilities causes
Doubling Season's ability to become applicable, and the remaining effect and the Season can be applied in either order. The final result depends on the order all three effects were applied. I'll be color-coding the results of the effects for ease of comprehension; apologies if this doesn't work for those looking at this response via email–it should be clear on the forums themselves, so you may wish to click through to see it there.
Applying the replacements in the order
Thing->
Biomancer->
Season or
Biomancer->
Thing->
Season means that both the ice and +1/+1 counters are doubled, and so gets the active player a final event of:
Put Thing in the Ice onto the battlefield with four eight ice counters and two four +1/+1 counters on it.
Applying the effects in the order
Thing->
Season->
Biomancer means that the ice counters get doubled, but the +1/+1 counters do not, for a final event of:
Put Thing in the Ice onto the battlefield with four eight ice counters and two +1/+1 counters on it.
And applying the effects in the order
Biomancer->
Season->
Thing means that the +1/+1 counters get doubled, but the ice counters do not, for a final event of:
Put Thing in the Ice onto the battlefield with four ice counters and two four +1/+1 counters on it.
This final option is probably going to be the one the active player will want to have happen.