Addison P. Wyman was famous for his descriptive parlor music, and this piece is a classic example of the 'character march.' It is notable for its rhythmic precision and celebratory tone.
At Henle 3 this is a late-beginner piece — comfortable hands-together playing is assumed, and musical shaping starts to matter. The main demands: fast passage work that stays light and even at tempo; a left hand with real melodic or rhythmic responsibility of its own; and precise articulation — the difference between crisp and blurred is the piece.
The main technical hurdle is keeping the left-hand chords precise and detached.
Comparable difficulty and character — good candidates for what to learn next.
A level or two down with the same spirit — ideal if this piece is still out of reach.
Where this piece's skills lead: slightly harder works making similar technical demands.
Christmas Bells March is rated Henle level 3 of 9 — late beginner repertoire, roughly ABRSM grades 4–5. In the RCM system it corresponds to about level 4.
You should be comfortable at Henle level 3 — meaning you can already play level 2–3 pieces cleanly. Learning it one level early is possible as a stretch piece, but more than that usually leads to months of frustration.
A typical performance of Christmas Bells March lasts about 4 minutes.
Christmas Bells March is available as free public-domain sheet music on IMSLP — the score is linked directly from this page.
Pieces at a comparable difficulty and character include 100. Yıl Marşı by Hakan Ali Toker, Brigadier-Marsch by Béla Kéler, Bunker Hill by Albert Von Tilzer — see the full similar-pieces list on this page.