While you can accomplish a lot with the mod tools alone, you'll need to use external software to create new assets like textures, models, and animations. Bungie traditionally used Photoshop, 3ds Max, and Maya. These days we can use free alternatives like GIMP, Krita, and Blender.

Texturing

Custom textures are created by converting TIFF images into bitmap tags using Tool. TIFF is widely supported and you can use any software that can save TIFFs without compression, with an alpha channel, and preserving RGB data where alpha is 0.

Modeling

Models and animations are most commonly made in Blender or and exported to source data format using the Halo Asset Blender Development Toolset and Foundry. Other 3D software like 3ds Max is supported using the FBX pipeline or legacy community exporters.

The official tool Sapien allows you place certain objects in a scenario but it's not a 3D modeling program. This is different from some other engines that have built-in level editors like UnrealEd and Source's Hammer. You will need to use external software like Blender to model your BSP.