Nicholas II' diary, April 1st, Saturday (Old Style):
'' ...During the day, we
began breaking the ice near the bridge; Tatiana, Valya and Nagorny worked..." He mentioned breaking the ice almost the whole April. So the official begining of breaking the ice would be April 1st 1917, since he wrote 'today
we began breaking the ice...'. The word 'ice' (Russian: led) is also mentioned on 3rd, 4th, 6th, 9th 23rd and 24th April. I found the Tsar's entry on Anna Vyrubova's arrest , it is 21 March and he afterwards mentions breaking the ice for the first time, on April 1st.
The name 'Derevenko' is mentioned only twice, in August and September and is reffered to the surgeon Vladimir Nikolaevich Derevenko and his son Kolya.
Also, we should believe that breaking the ice hadn't begun before April 1st. So,
the photo was taken after 21 March (OS).
Nicholas's diary would probably tell us what day the family began breaking up ice on the canals — if it was after 21 March/3 April, then I think we can dismiss Vyrubova's claim regarding Derevenko's behavior.