The documentation of themepark (support articles) mention something along the lines of:
We never released a patch as the game works perfectly if you the microsoft mouse driver.

i tried ms mouse drivers:
6.02 6.10 6.24 7.04 8.20 11.00

6.02 doesn't improve anything so no talking about it

as for the others:
mouse pointer disappears with all of them too.

as for freezing:
486 no longer freezes with turbo off
one exception is that if i configure 11.00 to use both mice: ps2 and com at the same time (previous versions didn't allow such a thing or i don't know a swich) i can freeze even 486dx40 with turbo on with ps2 mouse.

386 still freezes with turbo off with all of them
i can also rather easily freeze 386 with turbo on with: 6.02 6.10 6.24 7.04
never managed to freeze 8.20 11.00 with 386 turbo on

in dosbox and serial mouse you need to lower cycles to 500 to freeze them.

I am not sure whether dosbox is using ms drivers in booted dos this way:
i run serial driver so it wipes out ps2 driver
than i switch off serial driver so no mouse driver is installed
i install msdriver to ps2 (but it somewhat installs too quickly, so i don't know whether it really installs itself).

btw is there any /? /help for those old ms drivers? only 11.00 displays help and it somewhat matches the old ones but not everything.