diff --git a/airflow/providers/snowflake/hooks/snowflake.py b/airflow/providers/snowflake/hooks/snowflake.py
index 5bf94fae6984f..82373b65861f9 100644
--- a/airflow/providers/snowflake/hooks/snowflake.py
+++ b/airflow/providers/snowflake/hooks/snowflake.py
@@ -18,7 +18,7 @@
 import os
 from contextlib import closing
 from io import StringIO
-from typing import Any, Callable, Dict, Iterable, List, Optional, Union
+from typing import Any, Callable, Dict, List, Optional, Sequence, Union
 
 from cryptography.hazmat.backends import default_backend
 from cryptography.hazmat.primitives import serialization
@@ -262,7 +262,7 @@ def run(
         self,
         sql: Union[str, list],
         autocommit: bool = False,
-        parameters: Optional[Union[dict, Iterable]] = None,
+        parameters: Optional[Union[Sequence[Any], Dict[Any, Any]]] = None,
         handler: Optional[Callable] = None,
     ):
         """
@@ -290,7 +290,8 @@ def run(
                 sql = [sql_string for sql_string, _ in split_statements_tuple if sql_string]
 
             self.log.debug("Executing %d statements against Snowflake DB", len(sql))
-            with closing(conn.cursor(DictCursor)) as cur:
+            # SnowflakeCursor does not extend ContextManager, so we have to ignore mypy error here
+            with closing(conn.cursor(DictCursor)) as cur:  # type: ignore[type-var]
 
                 for sql_statement in sql:
 
diff --git a/setup.py b/setup.py
index ab4b5018ea249..2e4f3ef72fd69 100644
--- a/setup.py
+++ b/setup.py
@@ -510,13 +510,8 @@ def write_version(filename: str = os.path.join(*[my_dir, "airflow", "git_version
     'slack_sdk>=3.0.0',
 ]
 snowflake = [
-    # Snowflake connector 2.7.2 requires pyarrow >=6.0.0 but apache-beam requires < 6.0.0
-    # We should remove the limitation when apache-beam upgrades pyarrow
-    'snowflake-connector-python>=2.4.1,<2.7.2',
-    # The snowflake-alchemy 1.2.5 introduces a hard dependency on sqlalchemy>=1.4.0, but they didn't define
-    # this requirements in setup.py, so pip cannot figure out the correct set of dependencies.
-    # See: https://github.com/snowflakedb/snowflake-sqlalchemy/issues/234
-    'snowflake-sqlalchemy>=1.1.0,!=1.2.5',
+    'snowflake-connector-python>=2.4.1',
+    'snowflake-sqlalchemy>=1.1.0',
 ]
 spark = [
     'pyspark',