I believe that the caption for the hit point table is actually a typographical error that was never caught/rectified, with the following reasoning:
From the description of the Cavalier on page 14 of the Unearthed Arcana (Emphasis mine):
Such a character must be sponsored by a higher authority of greater status, and begins first as a 0-level Horseman (a retainer for a Knight), then a 0-level Lancer, and finally becomes a 1st-level Armiger of the cavalier class. The 0-level Horseman starts at -1500 experience points and has ld4 + 1 initial hit points. The Horseman becomes a Lancer at -500 experience points and gains another d4 roll for cumulative hit points. The Lancer becomes a 1st-level cavalier at 0 experience points, and gains another d4 in hit points. In contrast, a character whose social standing qualifies him or her for immediate
entrance into the cavalier class begins as a 1st-level Armiger with 1d10 + 3 hit points.
Additionally, in the subtext under the hit point table for the Cavalier on page 15, appears this:
If qualification for 1st level required progression through the two 0-level grades, then hit dice for 1st level are 3d4 + 1, but in all other cases 1d10 + 3 applies.
Under the description for the Paladin, it states:
The powers, abilities, and level advancement of the paladin as described in the Players Handbook remain unchanged. In addition, the paladin gains the abilities and powers of the cavalier class, including weapons of choice, parrying ability, horsemanship, saving throw bonuses, and immunity to fear.
The only place that I can find the reference to a 12 sided die for HP is in the table heading, leading me to believe that it is an error that was never noticed or rectified at the time. Even leading forward into 2e, the Paladin remains at 10, and Cavalier has changed into a kit as a subclass of fighter, so uses a d10 for hit point determination.
Checked Dragon magazine #72, and in both places that it references hit dice, it refers to them as d10:
\begin{array}{c c l}
\textbf{Class} &\textbf{HD Type} & \textbf {Maximum HD} & \textbf{Spell Ability} & \textbf{Level Limit} \\
\hline
\text{Cavalier} & \text{d10} &\text{10}^1 &\text{no} &\text{none} \\
\end{array}\begin{array}{l}
_{\text{— }^1 \text{Initial hit points for a 1st level cavalier range from 4-13 (generated either as d10+3 or 3d4+1), due to the }} \\
_\text{necessity of having to attain the social status necessary for 1st level.} \\
\end{array}
The HP chart also has a heading of 10 instead of 12 for the hit dice.