Hence there are reasons to run snow-covered lands instead of "normal" basic lands. Are there any reasons to run the regular basic lands instead of snow-covered lands? If not, then one might as well use snow-covered lands since it can conceivably bluff the opponent into thinking they're playing against a different deck, at least for the first turn.
There are plenty of cards that hose snow lands, in addition to the cards that @tehfurbolg posted.
- Avalanche is MLD that only targets snow lands.
- Cold Snap deals damage to each player during their upkeep equal to the number of snow lands they control.
- Freyalise's Radiance prevents snow permanents from untapping.
- Icequake and Thermokarst are land destruction that has an additional effect if the targeted land is a snow land.
- Legions of Lim-Dûl and Rime Dryad have Snow Landwalk.
- Rimefeather Owl has it's power and toughness equal to the number of snow permanents on the battlefield.
- Ronom Hulk has protection from Snow, which probably doesn't do much with snow basics but if the land gets animated then they can't block Ronom Hulk.
- The recntly spoiled "Reidane, God of Justice" // "Reidane's Shield" from Kaldheim has a static effect that causes snow lands your opponents control to enter the battlefield tapped
I believe the possibility of "normal" basics being better than snow-covered basics is very slim, but it exists. Some cards require an opponent or, more specifically, the defending player to control at least one snow land. An example is Ronom Serpent. In these cases it would be better for you to control no snow lands, but I would say for the most cases snow basics are (slightly) superior over "normal" basics.
You can find other cards like this by searching for "defending" and "snow" on scryfall.
One exception to this are decks playing Field of the Dead; that cares about lands with different names, which makes it very appealing to not go to snow basics completely but run a mix of snow and normal basics. As of late 2020, this is definitely not just a theoretical concern in Modern as Field of the Dead is very commonly played in the Tier 1 Primeval Titan decks.
@DenisS has given a good list of in-game reasons.
There is an out-of-game reason as well, namely cost. Regular basic lands have been printed so many times that they are in bountiful supply and quite cheap (unless you splurge and go for the full art ones). As of 2020, Snow-covered basic lands have only been printed in three sets (Ice Age, Coldsnap, and Modern Horizons), and thus have actual cost per card.
In 2020, this was at least a 10x price difference. A set of 500 regular basic lands sold for around $20, so $0.04 per card. Meanwhile, a set of 50 snow covered basic lands sold for around $25, so $0.50 per card. While not enormous, it's also not a trivial replacement. This is an extra $5 - $10 per deck (depending on how many basic lands you run). If you have no use at all for the snow mana, it's probably not worth it.
Additionally, there are many fewer art options for snow-covered lands. If you like pretty lands (Ravnica are my personal favorite) or if you like having lands that match the theme of your deck, there's not much to pick from in the snow-covered variety. As of 2020, Including secret lair drops (which are vastly more expensive), there are only 4 different art options for a snow-covered land (as each set only did one type of art for each), where basic lands have hundreds of art options.
There no real reason to use normal basics (there are things that you could argue on a technicality are reasons such as the cards listed in other answers that destroy snow permanents - but none of those reasons are applicable in usual play). It's like arguing that Forest is better than Tropical Island because Tropical island dies to Tsunami. It's technically true, but mostly irrelevant.
In fact there is a reason to always use snow basics in any format that allows them: As soon as you play a non-snow basic you've immediately revealed to your opponent that your deck does not contain Arcum's Astrolabe, or Ice-Fang Coatl, or anything else that references snow. Sure the uncertainty won't last long, but it may change decisions made in the first few turns that change the course of the whole match.
In other words strategically (except possibly in an open deck list tournament) you should always use snow basics if you really care about getting every possible last tiny sliver of advantage.