You are absolutely right, Georgiy: best not to read any fatalism into the Heir's last letter. He basically said 'How are you? How are (Various family members) and F-ff-fff-ff-feffera? (Probably a pet's name, with which Alexei Nikolaevich had a little fun) Greetings to the Botkins from all of us. I kiss you. Yours always, Alexei' and made a comically messy version of how he usually finished off his signature.
I have heard also that this was NOT, in fact, the last letter the Tsarevich sent to his friend -- that a little parcel containing a toy soldier with a gun was confiscated before Kolya Derevenko could get it. Because Alexei Nikolaevich had written, 'I send you my little gun' the Bolsheviks were suspicious that the Imperial Family had weapons - depriving Kolya of a birthday present from his friend, the last one the Tsarevich ever gave.