Is there any spell or magic item effect that can permanently freeze an area? (Freeze as in ice and snow).
The Ring of Winter, a powerful legendary artifact from Tomb of Annihilation, can permanently freeze areas (12 x 120 foot areas per day)
Since you mentioned "magic item effect", there's the Ring of Winter, a powerful legendary artifact from Tomb of Annihilation, which has the following in its stat block:
Magic. The Ring of Winter has 12 charges and regains all its expended charges daily at dawn. While wearing the ring, you can expend the necessary number of charged to activate one of the following properties:
- You can expend 1 charge as an action and use the ring to lower the temperature in a 120-foot-radius sphere centered on a point you can see within 300 feet of you. The temperature in that area drops 20 degrees per minute, to a minimum of -30 degrees Fahrenheit. Frost and ice begin to form on surfaces once the temperature drops below 32 degrees. This effect is permanent unless you use the ring to end it as an action, at which point the temperature in the areas returns to normal at a rate of 10 degrees per minute.
That feature seems to be what you're after, but if you want something on a larger scale:
Other Properties. The Ring of Winter is rumored to possess other properties that can be activated only by an evil being whose will the ring can't break. Frost giants have long believed that the ring can be used to freeze entire worlds, [...]
Although that last one is just hearsay, essentially, but the fact that it has been included in the stat block at least implies that it's possible to rule, as a DM, that it can do such things.
Mirage Arcane is an option.
Although Mirage Arcane produces an illusion of the desired, frozen terrain, the illusion:
includes audible, visual, tactile, and olfactory elements
Tactile elements would include the cold of the ice, frigid winds, etc, and even creatures that can see through the illusion would still feel those elements.
Although the duration of this spell is only 10 days, and not indefinite, any caster able to cast it (notably Bards, Druids, and Wizards) regains their spell slots on a long rest. Since you can take a long rest every 24 hours, you could keep up the frozen terrain by recasting Mirage Arcane on the area once every 10 days.
The best I can come up* with is control weather, but it's temporary
* regarding spells; see my other answer regarding magic items...
This is an 8th level spell that lasts for 8 hours, and allows you to control the weather within a 5 mile radius of your position, so long as you can see the sky for that duration (else the spell ends early).
From the PHB (p. 228):
You take control of the weather within 5 miles of your for the duration. You must be outdoors to cast this spell. Moving to a place where you don't have a clear path to the sky ends the spell early.
Wen you cast the spell, you change the current weather conditions, which are determined by the DM based on the climate and season. You can change precipitation, temperature and wind. It takes 1d4 x 10 minutes for the new conditions to take effect. Once they do so, you can change the conditions again. When the spell ends, the weather gradually returns to normal.
When you change the weather conditions, find a current condition on the following tables and change its stage by one, up or down. [...]
It then lists tables of precipitation, ranging from "Clear" to "Torrential rain, driving hail, or blizzard", temperature, between "Unbearable heat" and "Arctic cold", and wind, from "Calm" to "Storm".
Unless the area is already quite cold, you will have to change the weather step-by-step to get to Arctic cold, but I imagine a few hours of that, especially if you add a blizzard, should freeze most areas temporarily.
I guess if you had a circle of high level druids who all took it in turns to cast it every 8 hours, then you could create an indefinitely temporary tundra, which is as close to permanent as this spell is going to get...
Shape Water from Xanathar's Guide to Everything lets you freeze 2 small areas for 1 hour, 5x5x5 feet each. It's a cantrip. (XGE p.164) Depending on the size you want, you can have a bunch of elves who took the cantrip racial ability, or first level wizards fill a space. As a Canadian, I assume you are building a hockey rink?