Natural objects and decorations on a plane
For departures from the United States, TSA screens the object and what comes with it. Water around flowers, loose sand and pointed antlers each need a different packing decision. Your airline sets cabin size limits, while the destination sets import rules.
Flowers and planting materials
TSA allows fresh flowers through the checkpoint without water. If you carry a vase, assess any water under the liquids rules. Keep planting seeds in a closed, labelled packet so they are easy to identify. Soil and wet growing media need their own assessment; permission to carry seeds does not establish that they may be imported.
Sand, antlers and framed art
Seal sand before putting it in either bag. Cover the tips of antlers, and cushion a painting's frame and glass. Check the packed dimensions against your airline's cabin allowance. A large or awkward item may need to travel as checked baggage even when TSA generally permits the item through security.
Check entry rules separately
Security screening and border inspection answer different questions. If you are entering the United States, declare agricultural and wildlife products. USDA APHIS says that entry requirements for flowers, plants and seeds depend on the product and its origin; plants in soil cannot be brought in by travellers. Check the destination's rules before carrying any natural material across a border.
Sources: TSA: What Can I Bring?, USDA APHIS: plants, flowers and seeds for international travellers.