React these iron oxide, ammonium nitrate, and sucrose
Disclaimer: what I offer here is an educated guess.

$\ce{NH4NO3}$ is known to decompose quite easily, especially if proper catalyst is present. Thus, one of the reactions is

$\ce{NH_4NO_3 = N_2 + 2H_2O + [O]}$

generated oxygen may be used to oxidize sucrose or black iron oxide. I doubt that $\ce{N2O}$ is formed, since it is quite strong oxidizer and decomposes quite easily, especially if redox catalyst is present

$\ce{C_12H_22O_11 + 24[O] = 12 CO_2 + 11 H_2O}$

$\ce{2Fe3O4 +[O] = 3 Fe2O3}$

However, as you said, the snake is black, so the second reaction does not occur

the final process is dehydration of sugar, producing carbon (actually, the carbon may contain significant amount of hydrogen and oxygen)

$\ce{C_12H_22O_11 = 12 C + 11 H_2O}$

at the same time numerous other processes, producing gaseous reducing organics, happens, so I advise to use a fume hood.

When cooled, reducing atmosphere from sugar decomposition vanishes, and black iron oxide reacts with air

$\ce{4Fe3O4 +O2 = 6 Fe2O3}$

Since black iron oxide acts as a catalyst and does not melt on reaction conditions, it is good to use as fine one as you can get and maybe it may be used in smaller amounts. Since ammonium nitrate acts as main energy source here, it is likely that it can be used in larger amounts. Sucrose forms the body of the 'snake', so it may be used in smaller amount. 

The 'snake' consists of (partially) carbonized/caramelized sucrose binding other ashes together and leftovers from iron oxide. The expansion of volume results from gases emitted in the processes of decomposition of ammonium nitrate and decomposition of sucrose, though decomposition of ammonium nitrate is probably the main source here.

BTW, thanks for recipe, I think it would come handy for me this year.